1. Preheat oven to 375 degrees. Line a baking sheet with parchment paper. Cut squash in half lengthwise. Place on prepared baking sheet, cut side down. Cover with parchment paper and aluminum foil. Bake until tender, 1 to 1 1/2 hours. Let cool slightly; remove and discard the seeds, and scrape the pulp from the skin. Place the pulp in a large kitchen towel (not terrycloth), wrap it around the squash, and squeeze out approximately 3/4 cup of the juices.

2. In a large bowl, combine the squash pulp, egg, ricotta, Parmigiano, 2 teaspoons salt, and 1 1/3 cups flour. Mix with a wooden spoon or your hands until thoroughly blended together. Transfer the mixture to a lightly floured wooden board, and, with your hands, work gently into a dough, gradually adding a little more flour if the dough sticks too much to your hands and to the board. Dust the dough lightly with flour, and place in a bowl. Cover the bowl with a kitchen towel, and refrigerate for 2 to 3 hours.

3. To form the gnocchi, cut off a piece of dough about the size of an orange. Flour your hands lightly. Using both hands, roll out the piece of dough with a light back-and-forth motion into a rope about the thickness of your index finger. Cut the rope into 1-inch pieces. Hold a fork with the tines against the work surface, the curved part of the fork facing away. Starting from the bottom of the tines of the fork, press each piece of dough with your index finger firmly upward along the length of the tines, then let the gnocchi fall back onto the work surface. Repeat with the remaining dough until all the gnocchi have been formed. Transfer gnocchi to a lightly floured platter or baking sheet. The gnocchi can be cooked immediately or refrigerated, uncovered, overnight.

4. Bring a large pot of water to a boil over high heat. Add remaining tablespoon salt and gnocchi. Cover pot, and cook until water returns to a boil. Uncover, and cook until the gnocchi rise to the surface, 1 to 2 minutes. Let cook for just 20 to 30 seconds more.

5. While the gnocchi are cooking, make the sauce: Melt butter in a large skillet over medium heat. When it begins to foam, add sage, and stir a few times.

6. Remove the gnocchi from the pot with a slotted spoon or a skimmer, draining the excess water back into the pot, and place in the skillet. Season lightly with salt, and add a small handful of the Parmigiano. Stir over medium heat until the gnocchi are well coated with butter. Taste, adjust for seasoning, and serve immediately with a sprinkling of Parmigiano.