Put the mushrooms in a bowl and cover them with hot water. Set aside and allow them to soak to rehydrate them for at least 35 minutes. This step can be done a day ahead.
Combine the water and milk in a large saucepan; stir in the cornmeal and whisk it until it dissolves. Over medium-high heat, cook the cornmeal, whisking constantly until the polenta thickens and begins to leave the sides of the pan and forms a loose ball.
Scoop the polenta out onto a lightly oiled large cutting board or baking sheet and spread it evenly. Allow it to cool. It is best to refrigerate the polenta for an hour before slicing it or make it ahead and hold it covered overnight in the refrigerator.
Melt 1 tablespoon of butter in a sauté pan and cook the sausage until it is browned. Drain the mushrooms, reserving the water. Chop the mushrooms and add them to the pan with the sausage. Stir in the tomato sauce and cook for 20 minutes. Add 1/4 cup of the porcini liquid and cook 20 minutes longer. Season with salt and pepper.
Preheat the oven to 350°F. Butter a 9 X 12-inch casserole dish.
Spread a thin layer of the sausage sauce in the base of the casserole dish. Cut the polenta into 1/2-inch thick slices to fit the pan and make a layer in the casserole over the sauce. Spread more sauce over the polenta and sprinkle with some of the cheese.
Continue making layers, ending with the polenta and sprinkle the top with the remaining cheese and dot with the butter.
Bake until the cheese is nicely browned and the casserole is hot, about 25 to 30 minutes.
Let the casserole stand for about 5 minutes before cutting.
This recipe is featured on show 1811, Polenta Party Festa di Polenta.