2 pounds russet potatoes, peeled and cut into 1 inch cubes (about 6 cups)
3 pounds buttercup squash (about 1 squash) peeled, seeded, and cut into 1 inch cubes (about 8 cups)
6 tablespoons unsalted butter, plus more for the baking dish
1/2 cup heavy cream
1/4 teaspoon freshly ground nutmeg
1/2 cup finely grated Parmigiano-Reggiano cheese
10 amaretti cookies, crushed into fine crumbs (about 3/4 cup)
1. Cover the potatoes with cold water in a medium saucepan. Bring to a boil; add salt. Reduce heat to medium-high; cook the potatoes until soft, about 25 minutes. In another medium saucepan, cover the squash with cold water. Bring to a boil; add salt. Reduce heat to medium-high; cook until soft, 15 to 20 minutes. Drain the potatoes and squash separately.
2. Force the potatoes through a ricer into a bowl. In a separate bowl, mash the squash with a potato masher; stir in the potatoes.
3. Bring 4 tablespoons butter and the cream to a simmer in a small saucepan over medium heat. Add 1/2 teaspoon salt and the nutmeg. Season with pepper. Stir the cream mixture and 1/3 cup cheese into the potato mixture. Season with salt and pepper, if desired. Spoon into a buttered 10 inch round baking dish.
4. Preheat the oven to 350 degrees F. Add the remaining 2 tablespoons butter to the crushed cookies and stir to combine. Sprinkle the cookies over the casserole and add the remaining cheese. Bake until the topping is just browned, 20 to 30 minutes.