Preheat the oven to 400 degrees F.
Place the pumpkin or squash on a large baking tray, skin side down. Drizzle the oil over the flesh; season with salt and pepper, and roast for about 45 minutes or until the pumpkin is soft. Remove from the oven and allow it to cool for a few minutes. Scoop out the cooked pumpkin and place it in a food processor along with ½ of the cheese and the amaretti crumbs. Process until the mixture is smooth. Allow to cool while you are making the dough.
Heap the flour into a mound on a large clean dry board or work surface. Make a well in the center of the flour and break the eggs into the well. Add the salt. Start beating the eggs with a fork and gradually draw in the flour from the inside of the well. As the mixture begins to thicken, continue mixing with your hands. Add the water a little at a time, as needed. Knead the dough by pressing away from you with the heel of you hands and then fold it over toward you and repeat this action kneading for about 10minutes, or until the dough is smooth and elastic. Wrap the dough in plastic wrap and allow it to rest for at least 30 minutes. After the dough has rested coat the board with flour. Flatten the dough into a large disc and sprinkle it with flour. Roll the dough, turning it a quarter of a turn after each roll. Continue rolling until it is paper thin, about 1/8 - ¼ inch thick.
Bring a large quantity of salted water to a boil. Meanwhile, using a 2 ½ inch cookie cutter (or the rim of a glass) cut the dough into circles. Place about ½ tablespoon of the filling in the center of each circle. Using a pastry brush, paint the edges of the filled dough with water and fold over into a semicircle. Press down to seal the edges. Wet the edges of the semi-circle. Take the semi-circle of tortellini in your right hand and fold it around your left index finger so that the two ends meet, overlap the ends slightly and then press firmly down to secure making little “hats”. As you make the tortellini place them on a floured surface until the water boils. Drop the tortellini into the boiling water and cook for about 6 minutes or until they rise to the top of the water. Do not overcrowd the pot. If necessary cook the tortellini in two batches.
While the tortellini is cooking, melt the butter in a large fry pan; heat just until it starts to brown and add the sage. Be careful not to burn the butter. Place the drained tortellini into the fry pan with the melted butter and sage, cook for one minute. Carefully turn the tortellini to coat them with the sauce. Serve immediately with grated parmesan cheese.
Happily, butternut squash makes a perfect substitute for seasonally available pumpkin, because once you try this recipe you will want to make it over and over again all year long. Short on time? Try using wonton wrappers in place of the fresh pasta, they are a great substitute!