Bring the milk and broth to the boil with the bay leaf, add half of the herbs and let steep for 10 minutes. Pour through a sieve and briefly bring to the boil again. Now slowly trickle in the corn grits and stir. Then let it soak for 20 minutes.
Clean the vegetables and cut them into even pieces or slices. Halve tomatoes. Fry everything briefly in olive oil with the remaining herbs. Season the swollen polenta with salt, pepper, nutmeg and butter and spread on a small, greased baking sheet.
Spread the vegetables on the polenta and grate the fresh parmesan cheese over it. Bake in a preheated oven at 180 degrees top / bottom heat for about 20 minutes.