Prepare the Filling: In a medium bowl, combine the mashed butternut squash, eggs, Parmesan cheese, nutmeg, salt, and pepper. For the best texture, pass the cooked squash through a food mill or ricer before mixing.
Taste the mixture; if your squash isn't naturally sweet, add the sugar.
Adjust seasonings as needed. The filling should be smooth and flavorful.
Cut the Pasta: Lightly flour a work surface. Lay out a sheet of fresh pasta dough and cut it into 2 to 2. 5-inch (5 to 6 cm) squares.
Work with one sheet at a time, keeping the remaining dough covered to prevent it from drying out.
Fill and Shape the Tortellini: Lightly brush the pasta squares with a little water.
Place about 1 teaspoon (5 ml / 0.2 fl oz) of the squash filling in the center of each square.
Fold one corner over to the opposite corner to form a triangle, pressing firmly around the filling to seal the edges and remove any air pockets. Take the two bottom corners of the triangle and bring them together around your index finger, pressing one corner over the other to seal. Gently slide the tortellini off your finger.
Place the finished tortellini on a lightly floured baking sheet, making sure they don't touch.
Cook the Tortellini: Bring a large pot of generously salted water to a rolling boil. Carefully add the tortellini, cooking in batches of about 30 to avoid overcrowding the pot.
Cook for 3-5 minutes, or until they float to the surface and are tender.
Serve: Use a slotted spoon to remove the tortellini from the water.
Drain well and immediately toss with your favorite sauce, such as brown butter with sage leaves, and serve hot with an extra sprinkle of Parmesan cheese.
Roast, Don't Boil: For a richer, less watery filling, roast your butternut squash instead of boiling it. Halve the squash, scoop out the seeds, and bake at 400°F / 200°C until fork-tender.