Preheat oven to 450 degrees F.
Bring broth and milk to a boil. Stir in polenta slowly with a pinch of salt. Bring to a boil and then simmer until polenta begins to thicken, stirring constantly.
Add Parmesan cheese and basil. Salt and pepper, to taste. Once polenta is thick, remove from heat.
In a large pan, sauté onion, carrots, and garlic in olive oil for 1 minute. Add red pepper and mushrooms, sauté for 2 minutes. Add Swiss chard, herbs, and diced tomatoes. Continue to simmer until vegetables are soft. Drain vegetable mixture in a colander.
Cover the bottom of a lasagna-sized casserole dish with tomato sauce.
Spread drained veggies evenly in bottom of casserole.
Spread polenta on top of vegetables.
Top with mozzarella slices.
Cover loosely with aluminum foil. Bake for 30 minutes. Remove foil and continue baking until mozzarella begins to brown, about 15-20 minutes. Let rest for 5 minutes, cut into square portions and serve.
