Hahah, you stole everyone's dinner.
It's actually not random. The cooking minigame happens once you select Continue after one of three different dungeons: The Ghost Ship Cove, Old Capital or Ancient Temple. The food that is generated is based on which dungeon you just completed, combined with what different bosses you killed to get there.
It's poor form to take someone else's food or someone else's pot/pan (though it's kinda hilarious), unless you're solo or only have one other player or something. In those instances, you can each take two pots/pans so that you can stagger cooking and eating to maximize bonuses.
Stirring speeds up the cooking, and once there's no more stir option, the food is fully cooked. That's the best time to put it on your character's plate. There are three additives to the right that you can add to any dish to make it better (herbs?, salt, oil/sauce?). The different additives enhance the bonuses of the base food, but the actual calculations are unknown. People speculate that certain foods get better bonuses from certain additives. Obviously, burning the food is bad. Spoon in onto your plate, and click on the plate to begin eating. Click the plate quickly to eat faster.
Boss foods give the largest bonuses, and those also respawn the slowest. The Red Dragon, for example, doesn't respawn at all. So, it's in your best interest to beeline for one of the boss ingredients when given the opportunity.
The bonuses received at the end carry into the next dungeon. Of particular value is the score bonuses, since those will actually yield more experience once all is said and done.
