Gemara

(Beraisa - R. Shimon ben Yehudah citing R. Shimon): One may not eat meat and milk. One may benefit from it. It says "Ki Am Kodesh Atah... Lo Sevashel Gedi ba'Chalev Imo", similar to "v'Anshei Kodesh Tihyun Li u'Vasar ba'Sadeh Treifah Lo Sochelu";

Just like one may benefit from a Treifah but not eat it, the same applies to meat and milk.

Chulin 103b (Mishnah): One may not cook any kind of meat with milk, except for meat of fish and grasshoppers.

Inference: Our Tana forbids fowl with milk mid'Oraisa.

113a (Mishnah): One may not be cook meat of a Tahor Behemah with milk of a Tahor Behemah. (If they were cooked,) one may not benefit from it.

One may cook meat of a Tahor Behemah with milk of a Tamei Behemah, or vice-versa. One may benefit from it;

R. Akiva says, the Isur of a Chayah or bird (with milk) is not mid'Oraisa. It says three times "do not cook a kid in its mother's milk," to exclude Chayos, birds and Tamei Behemos.

R. Yosi ha'Galili says, it says "do not eat any Neveilah," and "do not cook a kid in its mother's milk." The Isur of Basar v'Chalav applies to species to which Neveilah applies.

Suggestion: Since Neveilah applies to birds, Basar v'Chalav should apply to birds!

Rejection: "In its mother's milk" excludes birds, which do not have milk.

115b (Tana d'Vei R. Yishmael): Three verses say "Lo Sevashel Gedi ba'Chalev Imo." They forbid eating, benefit and cooking.

(Mishnah): If one used the skin of the stomach to curdle milk, it is permitted;

If the milk absorbed the taste of meat, it is forbidden.

Avodah Zarah 35a - Question: Why did Chachamim forbid cheese of Nochrim?

Answer #1 (Shmuel): They curdle the milk in the skin of stomachs of Neveilos.

Answer #2 (Rav Chisda): They use vinegar to curdle.

Answer #3 (Rav Nachman bar Yitzchak): They use sap of Orlah to curdle.

Question: According to Rav Chisda and Rav Nachman, cheese of Nochrim should be Asur b'Hana'ah (for the curdling agent is Asur b'Hana'ah)!

This is left difficult.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 9:3): The Torah forbids only meat of a Tahor Behemah with milk of a Tahor Behemah, for it says "Lo Sevashel Gedi ba'Chalev Imo." One may cook meat of a Tahor Behemah with milk of a Tamei Behemah or vice-versa, and benefit from it. One is not liable offer eating it due to Basar v'Chalav.

Rambam (4): Similarly, the Torah does not forbid meat of a Chayah or bird in milk of a Chayah or Behemah. It is forbidden mid'Rabanan, lest people transgress and come to an Isur Torah of Basar v'Chalav, i.e. meat of a Tahor Behemah with milk of a Tahor Behemah. The Torah connotes only a kid in its actual mother's milk, therefore Chachamim forbade all Basar v'Chalav.

Rosh (Chulin 8:51): The Rif (42b) brought (the first Tana of the Mishnah (113a) and) R. Akiva, but not R. Yosi ha'Glili. This shows that he rules like R. Akiva. If he held that Chachamim argue with R. Akiva, he would rule like them, for we do not follow R. Akiva against a majority! Rather, he holds that the first Tana does not argue. The first Tana teaches that Basar v'Chalav applies only to Tahor species, and R. Akiva teaches the source to exclude Chayos, birds and Tamei species.

Mordechai (Avodah Zarah 827,828): The Gemara asked that cheese of Nochrim should be Asur b'Hana'ah according to Rav Chisda and Rav Nachman. It did not say so according to Shmuel, who says that they curdle in skin of stomachs. This shows that if Basar v'Chalav was forbidden through salting or pickling, only eating it is forbidden, but not Hana'ah. Some reject this. Therefore, we do not protest against one who permits, until there is a proof to forbid.

Rashi (Pesachim 44b DH Taru): The Torah permits to soak meat in milk the entire day and eat it, even if it gives taste. Only Derech Bishul is forbidden. However, mid'Rabanan it is forbidden.

Tosfos (Avodah Zarah 35a DH Mipnei): The Gemara said that we forbid cheese of Nochrim because they curdle in stomachs of Neveilos. Even in a stomach of a slaughtered animal, we should forbid due to Basar v'Chalav! We mentioned the Isur mid'Oraisa. There is no Isur mid'Oraisa of Basar v'Chalav here, since both are cold.

R. Akiva Eiger (on Shach 2): Tosfos answered that since it is only Basar v'Chalav mid'Rabanan, we are not concerned for a Safek. The Ri mi'Gash and Rambam answered that normally there is 60 times as much milk (as absorptions from the stomach), so there is no taste of meat. We forbid only because it curdled. Curdling does not make Basar v'Chalav. If so, there is no proof to permit Hana'ah from Basar v'Chalav mid'Rabanan. Since the Mordechai disagrees with the other answers, Tosfos' question remains. This requires investigation. Also, the Mordechai's answer, that one may benefit from what was pickled, is difficult. Also according to Tosfos, we should forbid to add cheese of Nochrim to a food and cook it, for if the cheese absorbed taste of meat through pickling, now he transgresses cooking it and it will be forbidden to eat the food! This requires investigation.

Tosfos (113a DH Basar): Likewise, Rabanan forbid fowl mid'Oraisa. Only R. Akiva holds that fowl and Chayos are not mid'Oraisa. We learn like it says below, that one may not cook with milk what is forbidden due to Neveilah (i.e. species to which Neveilah applies).

Agur (1054): We can prove that if Basar v'Chalav was forbidden through salting or pickling, only eating is forbidden, but not Hana'ah. Some disagree. Therefore, we do not protect against one who permits Hana'ah, since we do not find a proof to forbid.

Poskim

Shulchan Aruch (YD 87:1): Three verses say "Lo Sevashel Gedi ba'Chalev Imo." They forbid cooking, eating, and benefit. The Torah used an expression of cooking to forbid eating, to teach that mid'Oraisa it is forbidden only if cooked. Mid'Rabanan it is forbidden in every case.

Bach (2): The Rambam permits cooking and Hana'ah from meat of a Tahor Behemah with milk of a Tamei Behemah or vice-versa only mid'Oraisa. This is clear from his final words in Halachah like 3, and from Halachah 4. The Heter is only mid'Oraisa. Since mid'Rabanan one may not eat it, also cooking and Hana'ah are forbidden. They follow from the Isur to eat. The Rambam did not explicitly say that cooking and Hana'ah are forbidden mid'Rabanan because the Gemara did not explicitly say so. The Rambam's style is to leave his words indefinite like the words of the Gemara. The Gemara connotes that mid'Rabanan, only meat of fish and grasshoppers may be cooked with milk, so we should not be lenient. Also, Tosfos connotes that we hold like Rabanan. The Halachah does not follow R. Akiva against a majority. Even though the Rosh says that the Rif holds that R. Akiva explains the first Tana, but they do not argue, it is difficult to be lenient against Tosfos. Also Hagahos Sha'arei Dura says so. This is the custom, not to distinguish between birds, Chayos and Behemos regarding the Isur to eat. If so, we should not distinguish regarding cooking or Hana'ah mid'Rabanan. This is unlike the Rema.

Shach (2): Also the Mechaber (Sa'if 3) holds that fowl with milk, which is Asur to eat only mid'Rabanan, is Mutar b'Hana'ah even mid'Rabanan. Sefer ha'Chinuch says so, and the Rambam in Halachah 4 and Perush ha'Mishnayos. The Magid Mishneh, Maharshal and Acharonim explain explicitly say so, unlike the Bach, who says that the Rambam forbids Hana'ah.

Gra (1): Rashi (104b DH Maskif) says that the Torah forbids only Derech Bishul. This includes anything through fire. He excludes only pickling.

Gra (2): The Mishnah forbids milk that absorbed a taste of meat through curdling. Rashi and Tosfos say that this is mid'Rabanan.

R. Akiva Eiger (this is not in most editions of the Shulchan Aruch): The Pleisi (1) asked, according to the Rambam who holds that one is not lashed for Hana'ah from Basar v'Chalav, if so one of the verses "Lo Sevashel (Gedi ba'Chalev Imo)" is extra, for "Lo Sochal Kol To'evah" already forbids eating. R. Avahu holds that "Lo Sochal (Kol To'evah)" always forbids Hana'ah (Pesachim 21b), and the Rambam rules like this! I answer that if today one cooked half a Shi'ur of Basar v'Chalav, and later another Chetzi Shi'ur, one is not lashed for "Lo Sochal", for he did not transgress for cooking (a Shi'ur). If he ate a k'Zayis, he is lashed for eating it, due to Lo Sevashel. Actually, if one cooked Chetzi Shi'ur, and later another Chetzi Shi'ur, I am unsure if he is liable. Alternatively, we can answer that one is liable for "Lo Sochal" only in the normal way of Hana'ah, since it says 'Achilah.' Lo Sevashel obligates even abnormal Hana'ah. The Rambam rules like this (Hilchos Ma'achalos Asuros 14:10).

Rema (ibid.): One may benefit from any Basar v'Chalav that is forbidden only mid'Rabanan

Source (Gra 3): This is from the Mordechai.

Taz (1): The Yam Shel Shlomo (Chulin 8:100) disagrees with the Rambam and Mordechai, and is stringent about Hana'ah. We rely only on the Rishonim and Acharonim.

Bach (1): Mid'Rabanan it is forbidden to eat in every case, e.g. even through salting or pickling. One may benefit from it, like it says in 91:8