1 small pumpkin, or butternut or acorn squash (about 1 pound)
2 tablespoons extra virgin olive oil
1/2 cup grated Parmigiano-Reggiano, plus more for serving
1/2 teaspoon freshly grated nutmeg
2 tablespoons balsamic vinegar
Kosher salt and freshly ground black pepper, to taste
1/2 recipe basic pasta dough
8 tablespoons (1 stick) unsalted butter
8 fresh sage leaves
1 large amaretti cookie
Cut the squash in half, remove the seeds, drizzle with olive oil, and place on a baking sheet. Roast for 25 to 35 minutes or until the squash is very soft. Remove from the oven, let cool, then scoop out the flesh from the skin.
In a large bowl, combine the cooled squash, cheese, nutmeg, balsamic vinegar, and salt and pepper. Stir well to combine.
Roll out the pasta dough to the thinnest setting on a pasta machine. Using a biscuit cutter or water glass, cut out 2-inch circles. Pipe or carefully spoon a rounded tablespoon of filling onto the center of half of the rounds and over the filling with the second pasta round. Press the edges together firmly to seal.
Bring 6 quarts of water to a boil and add 2 tablespoons of salt. Drop the lune in the boiling water and cook for 2 minutes. While the pasta cooks, melt the butter in a 12 to 14 inch saute pan until it foams and subsides. Add 2 to 4 tablespoons of the pasta cooking water to the butter and whisk to emulsify. Drain the pasta and add it to the butter. Add the sage leaves and toss gently for 1 minute over medium heat to coat the pasta with sauce. Divide the lune among four warmed plates, grate the Parmigiano-Reggiano and amaretti over each plate, and serve immediately.