Gemara

(Mishnah): Bishul Akum (a food that a Nochri cooked) is forbidden.

(R. Chiya bar Aba): "Ochel ba'Kesef Tashbireni v'Achalti u'Mayim..." - just like we may drink water of Nochrim, which has not changed through fire, also we may eat their food only if it has not changed.

Objection: The Torah does not say that it depends on whether it changed through fire! Rather, Chachamim decreed against Bishul Akum. The verse is only an Asmachta.

Version #1 (in Sura - Rav Shmuel bar Rav Yitzchak citing Rav): Bishul Akum does not apply to anything that can be eaten raw.

Version #2 (in Pumbadisa - Rav Shmuel citing Rav): Bishul Akum does not apply to things that do not come on kings' tables to accompany bread.

They argue about small fish, mushrooms, and porridge.

(Rav Asi): Bishul Akum does not apply to small salted fish.

(Rav Yosef): If a Nochri made Kisa d'Harsena (fried fish oil with flour), it is forbidden due to Bishul Akum.

One might have thought that the primary ingredient is the oil. Rav Yosef teaches, the primary ingredient is the flour.

(Rav Berona): If a Nochri made a fire in a swamp, the locusts (that became roasted) are forbidden.

Question: Since he did not intend to cook, Bishul Akum does not apply!

R. Yochanan taught that anything cooked (by a Yisrael) like the food of Ben Drusa (a thief who used to eat food one third or one half cooked) is not considered Bishul Akum (if a Nochri finishes cooking it).

38b - Question: Are cooked dates of Nochrim forbidden?

Surely, sweet dates are permitted. They can be eaten raw! Surely, bitter dates are forbidden. They are eaten only cooked! The question is about medium dates (that are eaten raw only in pressed circumstances).

Answer (R. Asi): My Rebbi (Levi) forbids them.

59a - Question: In Gavla, R. Yochanan forbade lupines cooked by Nochrim, for the residents are not Bnei Torah (and are prone to treat Bishul Akum lightly).

He holds that letter of the law, Bishul Akum does not apply, even though they are not eaten raw. It applies only to what comes on kings' tables.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 17:9): Chachamim forbade to eat bread or cooked foods of Nochrim, even when there is no concern for forbidden absorptions, in order to distance Yisre'elim from Nochrim so they will not mingle and come to intermarriage

Rambam (14): If a Nochri cooked a food that is eaten raw, it is permitted. Chachamim decreed only on things that are not eaten raw.

Rambam (15): Chachamim forbade only things that go on a king's table to eat bread with them, such as meat, eggs and fish. Something does not come on kings' tables to eat bread with it, such as lupines that Nochrim cooked, are permitted, even though they are not eaten raw. The decree was primary due to intermarriage, lest the Nochri invite the Yisrael it a meal. One does not invite someone to eat something that does not come on kings' tables.

Rambam (19): If a Nochri cooked locusts unintentionally, they are permitted, even where they come on kings' tables for Parperes. (Some say that Parperes is an accompaniment for bread; some say that it is a dessert.)

Rosh (2:28): R. Tam rules like both versions to be lenient. We forbid due to Bishul Akum only what comes on kings' tables and it is not eaten raw. He learned from the Gemara, which said that the versions differ about things that are not eaten raw and do not come on kings' tables. Version #1 forbids, and Version #2 permits. It did not mention things that are eaten raw and come on kings' tables, which Version #1 permits and Version #2 forbids. This shows that we are lenient for both versions, so we listed only things that Version #2 permits (but Version #1 would forbid them). The Gemara knew that Version #2 comes to add (to what is permitted). Another proof is that below, we permit honey because it is eaten raw. R. Yochanan taught that anything cooked like the food of Ben Drusa is not considered Bishul Akum, and all the more so if it is eaten raw. On 59a, R. Yochanan holds that letter of the law, Bishul Akum does not apply to lupines, for they do not come on kings' tables.

Hagahos Ashri: The Rashbam forbids Bishul Akum lest the Nochri feed the Yisrael something forbidden (and the Yisrael will not realize, for it changed form). Something that changed through fire is forbidden, whether it was cooked in water or roasted. We are not concerned for something that was not changed through fire, for it is recognizable.

Ran (15a DH ul'Inyan): R. Tam rules that things that do not come on kings' tables to accompany bread are permitted, for R. Yochanan says so (59a). Even if Rav disagrees (according to Version #1), the Halachah follows R. Yochanan against Rav. Rav Asi taught that Bishul Akum does not apply to small salted fish. Do not infer that Bishul Akum applies to small unsalted fish, even though they do not go on a king's table. Perhaps fish that are naturally salty go on a king's table, and this is why Rav Asi needed to permit. Even if you could infer this, Rav Asi holds like Rav, but we rule like R. Yochanan. However, Bishul Akum does not apply even to what comes on kings' tables if it is eaten raw. The entire Sugya is like this. We permit honey because it is eaten raw. Version #2 comes to add another leniency. R. Chananel and the Rambam agree. The Ramban rules like Version #1, that Bishul Akum applies to anything not eaten raw, even if it does not go on a king's table. He learns from cooked dates of Nochrim. We forbid bitter and medium dates, since they are not eaten raw. The Ramban holds that they do not come on kings' tables. This is no proof. Perhaps they become sweet through cooking, and they come on kings' tables! Rather, Bishul Akum does not apply to anything that is eaten raw, or does not come on kings' tables, or did not change through fire. However, I did not see Rishonim permit whatever did not change through fire. The Rif brought Version #1 and Version #2, and did not give a ruling. The Gemara forbids Kisa d'Harsena because the flour is primary (and it is eaten raw). Tosfos derived that if a Nochri baker fried loaves in eggs, they are permitted, if there is no concern for Tamei (eggs). Even though Bishul Akum applies to eggs, the flour is primary. If a Nochri cooked something forbidden due to Bishul Akum in front of us, the Rashba says that the Keli must be Kashered. Even though we forbid the food only due to intermarriage, and this does not apply to absorptions, since the food itself was forbidden due to intermarriage, the absorptions are like it. It seems that Sefer ha'Terumos agrees. He forbids a dough of a fish pie, for it absorbs from the fish which is Asur due to Bishul Akum. Even though Chachamim permitted bread of Nochrim, and the oil is not intact, before it was absorbed it was forbidden. The dough absorbed Isur.

Poskim

Shulchan Aruch (YD 113:1): Something that is not eaten raw, and it come on kings' tables to accompany bread or for Parperes, if a Nochri cooked it, even in a Yisrael's Keli in the Yisrael's house, it is forbidden due to Bishul Akum.

Beis Yosef (DH Shelakos): A Mishnah (35b) forbids Shelakos of Nochrim. Rashi and the Rambam explain that this is anything a Nochri cooked, even in a Kosher Keli. We forbid due to concern for intermarriage. However, in the Gemara (38a) Rashi said that we are concerned lest the Yisrael regularly eat with the Nochri, and the Nochri will feed him Isur.

Beis Yosef (DH u'Mah she'Chosav): R. Avraham permitted if the Nochri cooked in the Yisrael's house. R. Tam did not agree. The Poskim wrote Stam that it is forbidden, which implies even in the Yisrael's house.

Bedek ha'Bayis: This is unlike R. Yerucham, who says that most Poskim permit.

Shach (1): The Mechaber did not say that it must have changed through fire. This is like the Rambam. The Rema agrees; in Sa'if 2 he permits peas because they do not come on kings' tables, but not because it was not changed through fire. I say that the Gemara is like the Ran and Rashi, Hagahos Ashri, who permit what was not changed through fire. It seems that the Rif (according to the Ran) and Ra'avan agree, but the other Poskim did not distinguish.

Note: I did not see where the Ran connotes that the Rif permits what was not changed through fire.

Shach (2): Isur v'Heter says that even though we say that one who eats innards is not human (Nedarim 54b), so it is not Chatichah ha'Reuyah Lehiskaved (a piece fitting to honor guests with), Bishul Akum applies to them. It applies to also to mushrooms.

Gra (3): The Gemara said that Bishul Akum could apply to locusts (if the Nochri intentionally cooked them). The Rambam explains that they are a Parperes.