The
4gamer wiki page about cooking says that you get the option to cook or boil, which gives different bonuses for some foods (like, a higher atk% vs a higher def% but otherwise equal).
There's a strategy to cooking, too. Your goal is to cook (and eat) as much stuff as possible without letting anything burn. You can speed up cooking by mixing it, so at start your goal should be to stagger your cooking times. If the pots are A, B, C, and D, put food in A and B, then mix A so it finishes faster. Once you serve A, put something else in A so now you'll have A and B alternating their finish times and you don't have to rush or worry about things burning and also have time to eat.
Oh, and the ingredients available depend on what level you just cleared. (You're eating what you killed.) And the seasonings provide a multiplier, with different seasonings affecting foods differently. It looks like a lot of fun, really.