Commentary for Avodah Zarah 75:19

Rashi's commentary: The rabbis decreed [that one must not eat "stewed" or cooked foodstuffs of a non-Jew] because of the concern lest they eat impure things. And more [than this concern] it seems that the reason [for this decree] is because of [the concern] of intermarriages [between Jews and non-Jews]. And thus [in] Chapter 5 of the Mishnah, the great Rabbi Abraham son of Rabbi David said certainly lashes [are given because] the sages forbade a non-Jew from cooking in his house [for a Jew], but if he [i.e. the non-Jew] cooks in the house of a Jew, there is no suspicion of either intermarriage or of eating impure things. But Rabbeinu Tam did not agree with him, that certainly when it comes to a non-Jew cooking, the sages did not divide the general principle [of forbidding food cooked by a non-Jew] between the domain of the Jew and the domain of the non-Jew, because there is always a suspicion lest one is not careful also in the home of the Jew in the same manner that one is careful in the home of the non-Jew

We have now gone too far afield from the verse. The verse does not even hint that the food cannot be cooked. Thus the Talmud admits that the prohibition of cooked food is only rabbinic in origin.

If the food can be eaten while it is raw, then cooking does not make it edible for it was edible before. Thus even if it is cooked by a non-Jew, a Jew can still eat it. An example would be, for instance, a tomato.

This is the second version of the above statement. If the food is not “fancy” enough to be put on the table of a king to be eaten with bread then the prohibition does not apply.

These foods can all be eaten raw, and therefore according to the first version, the prohibition of food cooked by non-Jews does not apply. But kings do eat these foods, so according to the second version these laws do apply. Thus the two versions would disagree about these foods and others like them.

Since small salted fish can be eaten raw, the laws of foods cooked by Gentiles do not apply.

R. Joseph states two laws about these little fish. First of all, if the non-Jew cooked them, the Jew may use them for eruv tavshilin. This is the meal that one begins to cook on erev Yom Tov, as if he is making it for Shabbat, that allows him to continue to cook on Yom Tov for Shabbat.
The second law is that if the non-Jew makes these fish into a fish-hash pie, the pie is prohibited because of the crust which was baked by the non-Jew.

According to Rav, if a non-Jew sets fire to the ground and the fire roasts some locusts the locusts may not be eaten.

The problem with Rav’s statement is that we can assume the non-Jew burned the ground of the uncleared field not in order to roast the locusts but in order to clear the ground. In cases like this, where the intention was not to cook but to clear some unwanted thing away, the cooked food should not be prohibited.

The Talmud resolves that Rav prohibited because once roasted one could not tell whether the locusts were clean or not. The fact that it happened to be a non-Jew that burned the field is not material. [We should note that this is a difficult resolution. Clearly when Rav issued his statement it was material].

The assumption here is that the person singed the head of the animal to remove the hair and not to cook it. Therefore, as long as the animal is kosher, the Jew can eat it even though the non-Jew performed a cooking activity with it.

The pumpkin, put into the oven by the Jew, was cooked by the non-Jew who threw a peg into the fire and then lit the stove. Therefore the pumpkin should be prohibited. But Ravina teaches us that his intention was not to cook the peg but to harden it, therefore the pumpkin is permitted. Again, we take the person’s intention into account.

Shmuel rules that if the non-Jew facilitates the speeding up of the cooking process, the food is not considered as having been cooked by a non-Jew.

The Talmud notes that the statement by Shmuel seems to contradict a ruling by R. Yohanan. R. Yohanan said that if the food had already been cooked a minimal amount (sufficient for the bandit Ben Drosai to eat it—we will discuss this more later) then the prohibition of being cooked by a non-Jew does not apply. But if the food was not yet cooked, then if the non-Jew does turn it over on the coals then the food is prohibited. This contradicts what Shmuel said before.
The resolution is that R. Yohanan was referring to a case where the non-Jew essentially began the cooking process by putting the pot in the oven. The Jew only put the food into the pot. But if the cooking process had already begun, then the prohibition of non-Jewish cooking does not apply. This seems to be a considerable leniency.

This baraita teaches that if the cooking process was begun by the Jew, the non-Jew would be allowed to continue the cooking. The food is prohibited only if the non-Jew begins the cooking process.
Again we can see how lenient the rabbis were with regard to this prohibition. My impression is that amoraic rabbis inherited a series of prohibitions that were created during a period in which there was a real fear of assimilation. Many of these prohibitions seem likely to have been created as early as the Second Temple period, when Hellenism was at its height. By amoraic times Jewish identity had more fully coalesced and those Jews who remained within the fold were not threatened by eating food cooked by non-Jews. Thus they could be lenient with regard to these rules.