loki is a man who enjoys complex flavors and gourmet food. he is especially fond of the combination of chocolate and spice as well as sweet and salty (such as salted caramel). he enjoys discovering layers of flavor and things that surprise him. he wants to be thrilled, even by such a mundane act as dining.
some of his favorite foods include:
asparagus & brussel sprouts (salted & roasted w/ strips of bacon)
seafood
cinnamon
apples, particularly in the form of bjórr (alcoholic cider)
cupcakes & similar sweet baked goods
pork or wild boar spit-roasted over an open fire
spicy Asian cuisine, particularly Thai
i always imagined that loki did most of the cooking when he went on hunting trips with his brother & friends because 1) he could control the temperature of the fire with his magic to ensure even cooking, 2) he has knowledge of & access to a lot of herbs for seasoning, 3) he has more of a mind for flavors than the others might (save for volstagg), and 4) he just plain enjoys it. he probably doesn’t do much cooking on asgard outside of hunting trips, but on midgard or anywhere where there’s not a cooking staff to provide meals, he really enjoys it.
i don’t imagine him eating a lot of vegan food, though he’d certainly incorporate vegetables. i imagine asgard does a lot of hunting, but also a lot of fishing as well with all the water that surrounds the city. and since they have those flying ships as seen in thor 2, it wouldn’t be such a difficult thing even though it seems asgard’s main city is set on a series of cliffs (much like berk in how to train your dragon.)