Clean and peel the carrots, clean and wash the zucchini. Cut the soft inside with the seeds out of the zucchini in a wedge shape. Finely dice both vegetables. Bring the broth to the boil and add the diced vegetables. Sprinkle in the corn grits, stirring constantly, and leave to swell for 5 minutes over a low heat.
Wash the thyme, shake well dry, then pluck the fine leaves and chop finely. Season the polenta with thyme, salt and pepper. Set aside some thyme for garnish.
Pour the corn grits into a greased, rectangular casserole dish (20 x 20 cm) and allow to cool for 10 minutes.
Preheat the oven to 200 ° C. Sprinkle the polenta with parmesan and drizzle with the melted butter. Bake in the hot oven on the second rack from the bottom for 10-15 minutes. Cut the polenta into cubes, garnish with thyme and serve with skewers on a plate lined with lettuce leaves.