Eggs
Eggs have an issue of bishul akum, as they are fit for a royal table and not eaten raw. Although they can be swallowed raw, which is why raw eggs are not muktzah on Shabbos (see Issue 350, par. 11), it is not a normal manner of eating them—it is considered eating with great difficulty (שו''ע סי' קי''ג סי''ד, ט''ז שם סקי''ד ).
Salmon
Salmon is a high-quality food fit for a royal table. Similarly, it is not eaten raw as is. Thus, all poskim hold it is subject to bishul akum when baked or cooked.
Smoked salmon. Smoked salmon is not a problem of bishul akum. The issur is specifically with cooking or baking; smoking is not a problem of bishul akum (see Issue 373, par. 25). However, it is important to note that sometimes there are other kashrus issues that can arise. Thus, one must ensure there are no other kashrus concerns with smoked salmon.
Cured salmon—“gravlax.” Just like smoked salmon (above, 18), cured salmon poses no concern of bishul akum.
Sushi
Many people in the world today eat sushi made with small pieces of raw salmon or tuna surrounded by rice and chopped vegetables wrapped in nori [seaweed]. What began as a dish traditionally only found in Eastern Asia became widespread today in every big city in the world as an accepted dish for sushi lovers.
Thus, modern-day poskim discuss whether this changes the status of salmon to be considered “eaten raw” since many people eat sushi raw. If true, this would avoid the issur of bishul akum. On the other hand, perhaps salmon retains its status, as will be explained.
Sushi. The consensus of the poskim is that if a non-Jew cooks actual salmon prepared as sushi, it is not bishul akum, as it is in fact eaten raw. Although it is only eaten raw in a mixture with other things, many poskim consider that to be “eaten raw” as well (מג''א סי' ר''ג סק''ד הובא בגליון מהרש''א סי' יו''ד סי' קי''ג לגבי זנגביל, מ''ב שם סקי''א, מו''ר בשו''ת שבט הקהתי ח''ה סי' קל''ד ).
The rice in the sushi is subject to the issur of bishul akum, as rice is certainly not eaten raw and is fit for a royal table.
Permitting all salmon. However, most poskim agree that if a non-Jew cooks regular salmon not eaten as sushi, it still involves the issur of bishul akum. The fact that people eat sushi with raw salmon does not transform all salmon in the world into food eaten raw, as it is still considered the minority manner of eating (אבני ישפה, שלחן מלכים, שו''ת משיב נבונים ח''ג סי' נ''ג, שו''ת מציון תצא תורה ח''א הל' מאכלי עכו''ם, ס' אהל יעקב סי' קי''ג אות ל''ב ).
Breakfast Cereal
Breakfast cereals eaten with milk, e.g., cornflakes, Rice Krispies, or the like, have no issue of bishul akum, as they are classified as foods unfit for a royal table. Even if dignified people would eat it for breakfast at home by themselves, they would not serve it to guests. Thus, it is classified as something not served at a royal table (לבושי עז סי' קי''ג ס''א סק''ד, שו''ת חיי הלוי ח''ד סי' נ' אות י').
Chestnuts, “Marroni”
Shelled. Shelled chestnuts are fit for a royal table. Thus, when they are cooked or roasted, there is a problem of bishul akum. If they are cooked via steam, it is a machlokes (cited in Issue 373, par. 26) whether there is an issur of bishul akum.
In-shell. If a chestnut still has its shell, it is technically unfit for a royal table. In that case, it would depend whether we consider if the type of food in a general sense is fit for a royal table or we focus on how it is in its current form, which is unfit for a royal table. Those who are meikel have poskim to rely on. This is relevant in areas in Europe where non-Jews sell in-shell, roasted chestnuts on the city streets.
Cholent
Does cholent have an issue of bishul akum? This is relevant when a baal habayis prepared the cholent ingredients in a pot on erev Shabbos and forgot to turn on the flame, and it is now bein hashemashos erev Shabbos, a time when amira l’akum is mutar. The shaila is whether cholent becomes assur from bishul akum. The real question is whether cholent is considered fit for a royal table, as most people in the world do not eat cholent and it is made from basic ingredients.
Fit for a royal table. In practice, the psak is that cholent is considered fit for a royal table since we view it as an important food, and if a non-Jew would taste it, he would eat it (הגר''ש וואזנר הובא בס' הבית בכשרותו סי' ג') [though he would not sense the neshama yeseira...]. Also, it contains meat and potatoes, which are both certainly fit for a royal table. Perhaps the barley and beans are not, but all in all, the dish as a whole is considered fit for a royal table, so when cooked by a non-Jew it is assur [unless one relies on the heteirim for a non-Jew to cook in a Jewish home—see the coming issue אי"ה ].
The fact that cholent is served at weddings is seemingly not enough to make it considered fit for a royal table, as it is not served as a portion at the tables. It is only a supplemental food for hungry bochurim and the general public. Similarly, the fact that it is eaten at Shabbos seudos does not determine its status (see Issue 374, par. 24).