Bishul Akum

(6) These are the things of gentiles that are forbidden but it is not forbidden to derive any benefit from them: Milk that was milked without a Jew watching, and the (gentiles') bread, and their oil. (Rabbi and his court permitted their oil). And the cooked foods, and pickled/preserved foods in which it is their custom to put wine and vinegar, and their minced fish (literal: sardines), brine that does not have fish floating in it, and the chileq fish, a leaf of asafoetida, and sal-conditum. These are the things of gentiles that are forbidden but it is not forbidden to derive any benefit from them.

AND THE COOKED FOODS:

From where are these things known? R' Chiya Bar Abba said in the name of R' Yochanan: The verse states [when the Israelites asked Sichon, king of Amora, when about to pass through his land (Devarim 2:28)], "You will provide me with food for money and I shall eat, and you will give me water for money and I shall drink." Like water: just as the water was unchanged from its original state, the food, too, would also only be that which was unchanged from its original state. [The Gemara asks:] What now, what about the wheat kernels that [a non-Jew] made into parched grain-- would they also be forbidden? And if you say that this is so, but it was taught in a Baraita that wheat kernels made into parched grain are permitted! [The response:] Rather, it is that the water was not changed from the form in which it was created, so, to, the food was not changed from its created form. [The Gemara asks again:] But what about wheat [that a not Jew has] ground into flour? Would they also be forbidden? And if you say that this is so, but it was taught in a Baraita that wheat kernels made into parched grain and their flour are permitted! [The response:] Rather, it it that the water was not changed from its creation form through fire, so, too, the food must not change from its created form through fire. [The Gemara asks again:] Does the verse mention fire? [The original opinion concedes:] Rather, [food cooked by gentiles] is forbidden by Rabbinic law, and this verse is just a textual support.

Rav Shmuel Bar Rav Yitzchak said in the name of Rav: Whatever can be eaten as it is in its raw state is not subject to the prohibition on food cooked by idol worshippers. In Sura, this was taught in that way. In Pumbedita, they teach it in this way: Rav Shmuel Bar Rav Yitzchak said in the name of Rav: Whatever is not eaten at the royal table as an accompaniment to bread is not subject to the prohibition on food cooked by idol worshippers. What is the practical difference between these two versions? The cases of small fish, and mushrooms, and porridge [which are not eaten raw but are not eaten at the royal table].

[...]

Rav Yehuda said in the name of Shmuel: If a Jew placed meat on top of coals, and an idol-worshipper came and turned it over, the meat is permitted. What is this case? If you say that, had the idol-worshipper not turned it, it would have cooked anyway, then it is an obvious ruling! Rather, do we not have to say then that the case is one in which, if the idol-worshipper had not turned it, it would not have cooked? But then why is it permitted? Isn't that, then, the cooked food of idol-worshippers? Rather, the ruling is necessary only for the case where, without the turning, it would have cooked in two hours, but now it will cook in one hour. You might have said that hastening the coking is a significant thing, and the ruling teaches us that, nevertheless, the meat is permitted. [...] It was similarly taught in a Baraita: A Jew may place meat on top of coal and an idol worshipper may come and turn it until the Jew has returned from the synagogue or the study hall, and he need not worry. And a [Jewish] woman may place a pot on top of the oven, and an idol-worshipper may come and stir it until she returns from the bathhouse or from the synagogue, and she need not worry.

It was asked: What is the law if the idol-worshipper placed the meat on the coals and a Jew turned it? Rav Nachman Bar Yitzchak said, kal v'chomer, if it is permitted when the cooking is completed by an idol-worshipper, then it is certainly permitted when it is completed by a Jew. And it was also stated [...] it is not forbidden unless the beginning and completion are done by an idol-worshipper.

(1) A food that is not eaten when it is raw, and would also served at a kings table, to spread on bread or as a dessert, which was cooked by a non-Jew, even in the pots of Jews and in the house of a Jew, it is forbidden because it was cooked by a non-Jew.

(2) If one mixed a food that is eaten even raw with a thing that is eaten when raw and a non-Jew cooked them – if the essence is of the food is subject to the prohibition of non-Jewish cooking, it is forbidden. If not, it is permitted.

(7) If the fire of the oven was only lit sufficiently for bread, but not for other things, this is not considered a lit oven, and fires are not considered lit unless they are at the specific needed temperature. Therefore, if one wants to cook in a pan in an oven of non-Jews, it is necessary that the Jew puts the pan in himself, to a place in the oven that is appropriate to cook in. Rema: And there are those that disagree and believe that lighting a fire or stoking the coals in any way with regards to cooking, as with bread, is sufficient, and that is our custom. And even stoking the fire without any particular intentions works. And there are those that say that even if the Jew did not stoke the fire, and did not throw in any wood chips, only that the non-Jew lit the oven from a fire that was lit by a Jew, that is permitted.