Gemara

(R. Avahu citing R. Yochanan): One is not lashed for benefit from any Isur in an abnormal way.

Support (R. Zeira - Mishnah): The only liquids of Orlah for which one is lashed (for drinking them) are wine and olive oil.

Inference: One is not lashed for juice of strawberries, dates and pomegranates.

Suggestion: This is because this is not the normal way to consume them!

Rejection (Abaye): The Mishnah does not exempt for consuming the fruits themselves abnormally. It exempts only for (the juice, which is) a mere secretion!

Berachos 38a (Mar bar Rav Ashi): One blesses sheha'Kol on date honey.

This is because it is a mere Zei'ah (secretion, or extract). It is not the essence of the fruit.

39a (Rav Papa): Clearly, water in which beets, turnips or any Shelakos (cooked vegetables) were cooked has the same blessing as the beets, turnips or Shelakos.

Question (Rav Papa): What is the blessing on water in which Shivsa (dill) was cooked?

Answer (Mishnah): Once Sheves gives taste to a cooked dish, Terumah and Tum'as Ochlim no longer apply to Sheves (for no taste remains in it).

This shows that it is to add taste. (Therefore, one blesses Borei Peri ha'Adamah.)

Rishonim

Rosh (Berachos 6:18): One blesses Borei Peri ha'Adamah on water in which beets, turnips or dill were cooked. Water of all Shelakos is like the Shelakos, even though it is merely the soup and taste of the vegetables. One blesses on them like on the vegetables themselves. This is unlike Peros. We say above that it is a mere secretion, for the liquid does not have the taste of the fruit. If one cooked the fruit and the taste entered the water, perhaps one blesses Borei Peri ha'Etz on it.

Rashba (38a DH Devash): If one cooked dates and honey exuded through cooking, it seems that since Terumah does not take effect on fruit juice other than wine and [olive] oil, this shows that it is not considered a beverage, rather, a mere secretion. It is unlike water in which vegetables or dill were cooked. They are normally eaten cooked, so the water in which they were cooked is like them. Anything not normally eaten cooked or squozen, rather, it is eaten intact, we do not say that its water is like it.

Tosfos (39a DH Mai): We bless on water of beets Borei Peri ha'Adamah. Even though it is only water and the taste of the vegetables, we bless like on the vegetables. Even though we say that fruit juice is a mere secretion, we can distinguish.

Poskim

Shulchan Aruch (OC 202:8): One blesses sheha'Kol on liquid that exudes from all fruits, except for grapes and olives.

Shulchan Aruch (10): If one soaked or cooked fruits in water, even though the taste of the fruit entered the water, one blesses only sheha'Kol on the water.

Taz (8): This is like the Rashba. The water is like the fruits only if it is normal to cook or soak them. Therefore, one blesses Borei Peri ha'Etz on prune soup, for it is normal to cook them.

Beis Yosef (DH v'Nir'eh): It seems that water of Shelakos are like Shelakos, whether he cooked or soaked them in water without cooking. If they gave taste to the water, one blesses Borei Peri ha'Adamah.

Mishnah Berurah (51): He discusses Peros soaked for 24 hours. Then, they often give taste to the water.

Mishnah Berurah (52): Kinds of Peros that are normally cooked, their water is like them, and one blesses Borei Peri ha'Etz on it. This is if they are planted with intent to eat them cooked or pickled. If they are normally eaten raw, just some people dry them and afterwards cook them, one blesses only sheha'Kol on their soup. This is even if everyone cooks them when they are dry, since they were not planted with this intent. The Chayei Adam says that where they grow many plums and cherries, it is mostly with intent to dry them, so one blesses Borei Peri ha'Etz on the soup.

Kaf ha'Chayim (69): Most Acharonim hold like the Magen Avraham, who requires that they are planted with intent to cook them.

Bi'ur Halachah (DH Al): The Shulchan Aruch connotes that one blesses Borei Peri ha'Etz on the fruits themselves. What the Magen Avraham brings from the Rashba clearly holds like this. We must say that they are good to eat raw and cooked. If not, also on the Peros one blesses only sheha'Kol (Sa'if 12). Even so, the soup is Borei Peri ha'Etz only if they are mainly eaten through cooking. Apples prove this. They are good to eat raw and cooked (Sa'if 12), and even so the Rashba explicitly says that one blesses sheha'Kol on their water, for they are normally eaten raw and not cooked. Regarding their water, the majority must be destined for this (cooking). Perhaps the Rashba admits to the Rosh when they are eaten equally cooked or raw, and argues only when they are good to eat cooked, but they are normally eaten raw. What the Rashba says about Shelakos connotes like this. The Rosh says that one always blesses Borei Peri ha'Etz. I.e. they need not be eaten primarily cooked, but they must be good to eat raw or cooked. If they are good to eat only raw, one blesses only sheha'Kol even on the Peros when they are cooked! Therefore, on water in which apples were soaked, all agree that one blesses only sheha'Kol. The apples themselves are not normally eaten soaked, and this ruins them, so one blesses sheha'Kol on them. Their water is no better than them. There is another reason to bless sheha'Kol; see the Magen Avraham on 205:2. (In Sa'if Katan 6, he says that if one does not cook with intent to drink the water, one blesses sheha'Kol.) The Chayei Adam rules like this.

Shulchan Aruch (ibid.): The Rosh says that if the taste of the fruit entered the water, perhaps one blesses Borei Peri ha'Etz.

Taz (9): The Rosh said 'perhaps'. This shows that it is a Safek. We should avoid the Safek and bless sheha'Kol! This is difficult, for the Tur in Siman 205 wrote about this Safek 'surely, one blesses on the water in which vegetables were cooked like on the vegetables themselves.'

R. Akiva Eiger: This is not difficult! There, the Tur discusses vegetables. No one argues about them, for the Gemara explicitly says that one blesses on the water like on the vegetables. Here we discuss fruit cooked in water!

Taz (9): It seems that the Tur holds that also here there is no Safek. Even though the Rosh wrote 'perhaps', he did not mean that it is a Safek. I can say that he follows Tosfos, who said that perhaps we can distinguish (between water that absorbed the taste of the vegetables and fruit juice). Tosfos did not say what the distinction is. The Rosh says that perhaps this is the distinction (water in which fruits are cooked do not get the taste of the fruit), but there is no Safek about the law. Beet water is like beets, just like fruit juice is like the fruits. L'Halachah, one blesses sheha'Kol on those that are not normally cooked or minced. If it is normally cooked, one blesses Borei Peri ha'Etz. Do not ask why in this Siman we follow the majority, and not the taste. Here it is mere water, and it is not significant against the taste of the fruits.

Bach (Sof DH v'Im): However, for dry fruits such as apples, pears, cherries, and prunes, all agree that one blesses Borei Peri ha'Etz on their water, for they are normally cooked and not eaten intact.

Magen Avraham (22): This is difficult. It seems that the Rashba's reason is because they are normally cooked, therefore they are planted with intent for this. If so, Peros that are not planted with such intent, even if they were dried afterwards, it does not help. The Levush says that only fruits normally eaten cooked, one blesses Borei Peri ha'Etz (on their water). I found that the Maharshal wrote like this.

Magen Avraham (23): The taste enters the water through cooking more than if one squeezed the fruit itself.

Gra: The Rosh holds that the taste comes out through cooking, but not through squeezing. The Rashba holds that it is normal to cook vegetables (therefore the soup is like the vegetables), but it is not normal to cook or squeeze fruits.

Mishnah Berurah (53): This is when one tastes the fruit in the water in which it was cooked or soaked. We do not say that it is a weak taste and a mere secretion, the way we say about fruit juice (Sa'if 8). More taste enters through cooking than through squeezing raw fruits. The Acharonim say that one should bless sheha'Kol, but if he blessed Borei Peri ha'Etz, he was Yotzei.

Kaf ha'Chayim (70): Perach Mateh Aharon and Shevus Yakov say that one blesses sheha'Kol on coffee and tea. Hilchos Ketanos and Panim Me'iros say that one should bless Borei Peri ha'Adamah, but the custom is to bless sheha'Kol. Mor u'Ketzi'ah asked that if the water is like the Peri, one blesses Borei Peri ha'Etz, for it grows from a tree! In any case one blesses sheha'Kol. Pachad Yitzchak and Zera Avraham say to bless sheha'Kol on chocolate.

Kaf ha'Chayim (73): To avoid the Safek, one blesses sheha'Kol beforehand. The only way to avoid the Safek about the Berachah Acharonah (if they are of the seven species) is to eat them in a meal, or eat a fruit of the seven species and also drink water and bless after them. If one ate fruit of the seven species and drank fruit soup from other species, according to the Rosh me'Ein Shalosh exempts the soup, but according to the Rashba it does not. Therefore, one should first bless Borei Nefashos, and then me'Ein Shalosh. If he blessed me'Ein Shalosh first, he cannot bless Borei Nefashos now. He can drink water if he is thirsty, or eat something for which the Berachah Acharonah is Borei Nefashos and intend also for the soup.

Kaf ha'Chayim (74): The Shulchan Aruch connotes that according to the Rosh, it suffices if the taste entered, even if it was not soaked for 24 hours. However, Olas Tamid requires 24 hours. Eliyahu Rabah agreed. Mishbetzos Zahav says that if they were pickled in vinegar for the time to boil them on the fire, even if they are normally eaten like this, one blesses sheha'Kol, for perhaps the Shi'ur for pickling is longer. This is the Shi'ur for pickling in salted brine, so if this is normal, one surely blesses Borei Peri ha'Etz.

Kaf ha'Chayim (78): The soup is primarily water, even if it changed form. Therefore, one who eats the Peros outside a meal must wash his hands.

Shulchan Aruch (205:3): If one squoze vegetables, he blesses only sheha'Kol on the juice.

Taz (6) The Tur wrote 'my brother R. Yechiel says that one blesses the same Berachah as on the vegetables. I disagree. Surely, they changed for the worse. A proof is from liquid that come from fruits. One blesses sheha'Kol, but if he cooked them one blesses Borei Peri ha'Etz on the soup.' Clearly, more comes out through squeezing and all the more so through crushing, than what comes out by itself. It seems that squeezing or crushing is like cooking. This is no proof for the Tur. There, what comes out by itself is mere Zei'ah. It seems that R. Yechiel is correct, but one should not be lenient against the Tur. One should bless sheha'Kol. It seems that the Tur would agree that through crushing, what comes out is like the fruit itself. Surely it is like cooking.