For the Pasta Dough

1. Weigh the flour, or spoon it into a measuring cup and level with a knife. Do not tamp or tap.
2. Mound the flour on the counter, make a well, and add the eggs. Beat with a fork until well mixed.
3. Gradually incorporate the flour into the eggs, using a pastry scraper to prevent spillage.
4. Knead the dough for 3 minutes, adding more flour if necessary. Continue kneading for 10 minutes, or until satiny, smooth, and elastic.
5. Wrap the dough in plastic wrap and let it rest at room temperature for 30 minutes to 3 hours.
6. Work with one-fifth of the dough at a time, keeping the rest wrapped.
7. Lightly flour the machine rollers and work surface. Set the rollers at the widest setting.
8. Flatten the dough into a thick patty and guide it through the rollers five to six times, folding it in thirds each time.
9. Repeat at successively narrower settings, passing the dough through three times at each setting and folding it in half each time.
10. If the dough tears or is lumpy, lightly flour it and continue rolling.

For the Squash Filling

1. Preheat oven to 375°F (190°C). Lightly oil a baking sheet.
2. Cut squash in half, scoop out seeds, and place cut-side down on the baking sheet.
3. Bake for 1 hour, or until easily pierced with a knife. Let cool.
4. Scoop out the squash flesh, mash it, and stir in cheese and a little nutmeg.

For the Cappellacci

1. Roll out the pasta dough thinly. Cut 3 1/2 to 4-inch squares.
2. Place a spoonful of filling in the center of each square. Fold in half to form a triangle, and seal the edges.
3. Form an oversize tortellino by bringing the two ends together and sealing. Place on a floured baking sheet.
4. Melt butter with sage leaves in a saucepan. Brown the butter for a nutty flavor (optional).
5. Bring a large pot of salted water to a boil.
6. Cook cappellacci in batches for about 3 minutes, until tender but firm.
7. Remove with a spider or slotted spoon, allowing water to drain.
8. Place in warm serving bowls, sprinkle with cheese, and top with melted butter.
9. Season with salt and pepper and garnish with fresh sage leaves.