Baked Butternut Squash-and-Cheese Polenta

Preheat the oven to 375°. Arrange the squash on a large oiled baking sheet and roast for 30 minutes, until tender. Transfer the squash to a bowl and mash coarsely. (You should have about 1 1/2 cups.) Spread the pine nuts on a pie plate and toast in the oven for 4 minutes, until golden. Coarsely chop the nuts. Meanwhile, in a skillet, heat the 2 tablespoons of olive oil. Add the onion and sage and season with salt and pepper. Cover and cook over moderate heat, stirring, until golden, 25 minutes; add a few tablespoons of water if the onion looks dry. In a saucepan, bring the 6 cups of water to a boil. Whisk in the polenta and 1 teaspoon of salt. Cook over very low heat, stirring frequently, until tender, about 35 minutes. Stir in 1 tablespoon of butter along with the mashed squash, pine nuts, onion, Gouda and half of the grated Parmigiano cheese. Pour the hot polenta into a buttered large cast-iron skillet. Flatten the top of the polenta slightly without spreading it to the edges; refrigerate until firm, about 3 hours. Rub the surface of the polenta with softened butter and sprinkle with the remaining grated Parmigiano cheese. Bake in a 375° oven for 1 hour, until the top and side are lightly browned and crisp. Let stand for 20 minutes before cutting it into wedges.