Preheat the oven to 375 degrees F or 190 degrees C.
In a large skillet over a medium heat, add the ground beef, onion, zucchini, carrot, peppers and garlic with some salt and pepper to taste and sauté until the meat is browned and the veggies are wilted.
Add the hotdogs to the pan and sauté just until they begin to develop a slight color.
Add the salsa, water, beans, brown sugar, and chili powder, stir it together and let it simmer uncovered for 10 minutes while you make the polenta.
Add the water, milk, butter and salt to a medium saucepan and bring up to a boil.
Lower the heat then add the polenta while whisking to avoid lumps and simmer for 3 minutes. Turn off the heat, stir in the cheese and set aside.
Spoon the chili into a greased 9x12-inch casserole dish. Top with the polenta and bake at 375 degrees F or 190 degrees C for 25 minutes