Indeed when the majority of ingredients in a dish can be eaten raw, the food is exempt from bishul akum
OU Kosher gives the details here
Shulchan Aruch (Y.D. 113:2) says that if a non-Jew cooked a mixture
that contained some ingredients that can be eaten raw and some
ingredients that require cooking, one needs to determine which
ingredients are the ikar [main] and which are tafel [subsidiary].
If the ikar ingredients
can be eaten raw then the food as a whole is viewed as edible raw and
is exempt from bishul akum. If however, the ikar ingredients require
cooking, then this food requires bishul Yisroel. If none of the
ingredients are clearly the ikar ingredients, then we follow the rov
Note however that vegetables require checking for bugs, which is a very significant prohibition, and some ingredients you mention (specifically cheese) require kosher supervision. Last, cooking with onions creates additional complexity in case one mixes milk and meat utensils. As such, one needs to be extremely careful should this situation occur in practice.
Of course, consult your rabbi
before implementing anything you learn here.