Bring the water to a boil with 1 tablespoon salt, and slowly stir in the cornmeal in a thin, steady stream. Cook, stirring occasionally, for 20 minutes, until polenta is stiff and leaves the sides of the pan. Spread in a baking dish to a depth of 1 1/2 to 2 inches. Keep warm in a 250 degree oven while making the sauce.
For the sauce, heat 3 tablespoons of the oil in a saucepan, add the onion, and cook over medium heat until soft. Add the sausages and cook another 3-4 minute; stir in the mushrooms and cook 2 minutes more. Add the tomato sauce, basil, and salt to taste. Cover and simmer for 30 minutes. If the sauce becomes too thick, add 1/2 cup water, stir, and continue to cook. Add the remaining 3 tablespoons oil and cook 10 minutes more.
Remove the polenta from the oven and dot with cubes of the cheese. Turn oven up to 350 degrees and bake the polenta and cheese until it is ho and the cheese is melted. Cut in squares and spoon the sauce over the top.