In a large bowl, add the butternut squash purée, mascarpone, salt, pepper, nutmeg and Parmesan and mix until combined. Set aside until ready to use.
Fill a deep pot with heavily salted water and bring to a boil.
Place 1 tablespoon of filling onto half of a rolled out pasta sheet. Repeat with 2 more tablespoonfuls. Fold the other half of the pasta sheet over to cover the filling. Lightly press down around each mound of the filling to seal the ravioli. Using a pastry cutter or knife, cut around each mound of filling to make 1 1/2-inch squares. Crimp the edges to seal.
In a small saucepan over medium heat, warm the butter until melted, stirring constantly. Continue cooking the butter, until all of the milk solids turn golden and the butter has a nutty fragrance.
Gently drop the ravioli into the boiling water and cook for 3 to 5 minutes. Using a spider or slotted spoon, transfer the ravioli to a serving dish.
Drizzle the brown butter over the ravioli, garnish with shaved Parmesan and serve immediately. Enjoy!