Steps

1. Make the mushroom sauce and set it aside.
2. While the sauce cooks, make the polenta.
3. Coat the bottom of a dish with enough mushroom sauce to cover. Sprinkle it with about 2 tablespoons of the Parmesan and ¼ cup of the Fontina. Spoon about half of the warm polenta into the dish and smooth it into an even layer. Spoon half of the remaining sauce over the polenta in a smooth layer. Sprinkle with 3 more tablespoons of Parmesan cheese and about ⅓ cup of the Fontina. Pour the rest of the polenta on top and smooth it with a spoon to level it. Pour on the rest of the sauce, spreading it so that the polenta is entirely covered. Sprinkle with 3 more tablespoons Parmesan and the remaining ⅔ cup Fontina. Dot all over the top with bits of butter.
4. Bake the pasticciata until a golden-brown crust forms on top, about 30 minutes. Remove it from the oven and let it stand for 5 minutes to firm up before serving.