This elegant dish has become a popular offering on Italian trattoria menus. It features a multitude of flavors—squashy, sweet, savory, buttery, herbal, and nutty—working together to create complexity, and contrasting textures—silky filling and pasta, crunchy nuts—to add interest. The butternut squash must first be cooked to drive off excess moisture and render it soft and velvety; we use a microwave to expedite and simplify the squash-cooking process. Grated Parmesan cheese in the filling not only adds flavor, it also acts as a binder that holds the filling together. The browned butter sauce is simple, but very rich. This dish is best served in small portions either as a first course or a pasta course before the main dish. This recipe uses fresh pasta from the Fresh Pasta recipe. If you haven't already done so, you'll need to make the fresh pasta. You will need a food processor and pasta machine in order to prepare the pasta. To be as efficient as possible, make the pasta dough, prepare the squash filling while the dough rests, then roll out the dough while the squash is in the refrigerator. By the time the dough has been rolled out into thin sheets, the filling will be cool enough to use.