According to the Mishnah (38b), in addition to non-Jewish milk, oil and bread (see the discussions on daf, or page 35and daf 36), there were other problematic situations related to eating food prepared by non-Jews. One of the specific things that are mentioned are shelakot – cooked vegetables. This is the source for the general prohibition against eating bishul akum – food cooked by non-Jews.
While the Gemara first associates this prohibition with a passage in the Torah – Rabbi Hiyya bar Abba quotes Rabbi Yohanan as teaching that this is based on Devarim 2:28, where Moshe offered to purchase limited types of food and water from the nations in the desert as the Children of Israel passed through their land – nevertheless the Gemara concludes that it is a prohibition of Rabbinic origin.
In the Mishnah, Rashi explains that the underlying reason for this prohibition was similar to that of the prohibitions against the use of non-Jewish milk and bread – a concern lest it lead to a close relationship that would lead to marriage and assimilation. Nevertheless, Rashi on our daf offers an alternative explanation – that we are afraid that eating food prepared by non-Jews will lead to a situation where the non-Jew may put non-kosher ingredients into the food.
There are two limitations brought by the Gemara to this prohibition in the name of Rav Shmuel bar Rav Yitzhak quoting Rav –
1. In Sura they taught that anything that is eaten raw does not fall into this category
2. In Pumbedita they taught that anything that is not important enough to be served at the king’s table is not included in this category.
Both of these limitations are accepted as the halakhah, so only food that is important enough to be served at a royal table and is not eaten raw will be forbidden if cooked by a non-Jew with no direct participation of a Jewish person. Today it is common practice for the kashrut supervisor to turn on the ovens at the beginning of the work day in order to ensure that the food is considered bishul yisrael.