The Sages forbade food cooked by a non-Jew (בישולי עכו״ם) — out of concern for closeness (חתנות) — but only if it meets two conditions: it is not edible raw AND it is fit for the table of kings (עולה על שלחן מלכים). The Jew's participation in the cooking (lighting the fire, stoking, placing, stirring) removes the prohibition; it is enough that the Jew brought it to maachal ben drusai (a third of the cooking); and salting, smoking and pickling do not count as "cooking" (Shulchan Aruch, Yoreh De'ah 113 — 16 se'ifim)
דָּבָר שֶׁאֵינוֹ נֶאֱכָל כְּמוֹ שֶׁהוּא חַי, וְגַם עוֹלֶה עַל שֻׁלְחַן מְלָכִים לְלַפֵּת בּוֹ אֶת הַפַּת אוֹ לְפַרְפֶּרֶת, שֶׁבִּשְּׁלוֹ עוֹבֵד כּוֹכָבִים — אֲפִלּוּ בִּכְלִי יִשְׂרָאֵל וּבְבֵית יִשְׂרָאֵל — אָסוּר מִשּׁוּם בִּשּׁוּלֵי עוֹבֵד כּוֹכָבִים.
A thing that is not eaten as it is, raw, and that moreover comes up on the table of kings to accompany bread or as a delicacy, which a non-Jew cooked — even in a Jew's vessel and in a Jew's house — is forbidden as bishul akum.
Shulchan Aruch, Yoreh De'ah 113:1LEVEL 01
Hebrew text of the 16 se'ifim with a fluent English translation. The two conditions of bishul akum, the kings' table, the Jew's participation (חיתוי), maachal ben drusai and salting / smoking / pickling which are not cooking, explained with practical cases.
📖 StudyLEVEL 02
In-depth pilpul: the sugya of Avoda Zara, the yesod of the dual criterion of se'if 1 (נשתנה ע״י האור — Rashi/Ran/Rif vs Rambam), the שומן בעין that is not nullified, the מחלוקת on שגירה / חיתוי (se'if 7), acquired vs hired maidservants, חקירות and נפקא מינות.
📖 StudyLEVEL 03
Comparative tables (the 2 conditions, Mechaber vs Rama on participation, maachal ben drusai reached or not, מליחה / עישון / כבוש vs cooking), golden rules, classic pitfalls (עיקר, שומן בעין, ספק ביש״ע, the egg) and memorization of the 16 se'ifim.
📖 StudyLEVEL 04
The practical halacha according to the Shach, Taz, Pri Megadim and Pitchei Teshuva, then the Sephardic poskim (Yabia Omer, Yalkut Yosef, Or LeTzion) and Ashkenazi poskim: industrial ready-meals and restaurants under certification (the mashgiach who lights the fire), canned goods, coffee and tea, cooked eggs, the Sephardic (הנחה) / Ashkenazi (חיתוי) distinction. A level of psak, not "Daat HaRav".
📖 StudyAccording to the Shulchan Aruch (YD 113:1), food cooked by a non-Jew is forbidden as bishul akum only if it meets two conditions: (a) it is not eaten as it is, raw (אינו נאכל כמו שהוא חי), and (b) it comes up on the table of kings (עולה על שלחן מלכים) to accompany bread or as a delicacy. The prohibition, whose reason is closeness (חתנות), applies even when cooked in a Jew's vessel and in a Jew's house. For practical halacha, consult your Rav.
Yes. Anything a Jew cooked a little, at the beginning or at the end (se'if 6), is permitted — even if it would not have cooked without the non-Jew. For the Mechaber, the Jew must at least place the dish (הנחה); for the Rama and the custom, it is enough that the Jew lights the fire or stokes the coals (חיתוי), even without intent (se'if 7). And it is enough that the Jew brought it to maachal ben drusai — a third of the cooking — for the non-Jew to finish. For practical halacha, consult your Rav.
No (se'if 13). A fish salted by a non-Jew and fruit smoked until edible are permitted, for salting is not like boiling (מליח אינו כרותח) and smoking is not like cooking (מעושן אינו כמבושל); the Rama adds that pickling (כבוש) is likewise not like cooking, for only cooking by fire was forbidden. However, that which is eaten raw only with difficulty — large salted fish, salted meat, an egg, bitter dates (se'ifim 12-15) — is forbidden if a non-Jew cooked it. For practical halacha, consult your Rav.