In a 12 to 14-inch saute pan, heat 2 tablespoons oil over medium-high heat. Add the sausages and cook, turning occasionally, until all sides are browned and the fat runs freely from each sausage. Remove and discard the excess fat, then add the tomato sauce with the sausages, scraping the bottom to incorporate any browned bits. Season with salt and pepper, if necessary, reduce the heat to a low simmer, and cook, covered, for 1 1/2 hours, stirring occasionally.
Remove the sausages from the sauce to a cutting board, slice, and set aside, along with the sauce.
Bring 2 quarts of water to a boil in a large pot over high heat, and add the sea salt and remaining 1 tablespoon of oil. Stir in the cornmeal, a little at a time, whisking constantly to prevent the formation of lumps. Cook for 5 minutes, until the polenta comes away from the sides of the saucepan. Turn the polenta out onto a clean wooden board and allow to cool. Once it is cool, cut it into strips, using butcher's twine or a very sharp knife.
Preheat the oven to 400 degrees F.
Cover the bottom of a 9 by 13-inch oven-proof casserole or baking dish with a layer of sauce. Add a layer of polenta slices, then a layer of cheese, a layer of mozzarella, and a layer of sliced sausage. Repeat the process until all the ingredients have been used, ending with a layer of cheese. Bake in the oven 25 minutes. Let sit 5 minutes before serving.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot and cook until the carrot is quite soft, about 5 minutes more. Add the tomatoes and their juice and bring to a boil, stirring often. Lower the heat and simmer until as thick as hot cereal, about 30 minutes. Season with salt, to taste.
This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.
Recipe copyright Mario Batali, 2002. All Rights Reserved.