Preheat oven to 400°F. Cut squash in half lengthwise. Using a spoon, remove the seeds. Place squash halves on a baking sheet (cut side up) and cover flesh with olive oil. Add salt, garlic and sage. Roast until squash is very tender and coloured on the ends. Cool slightly. Peel the squash halves and place the flesh in a blender or food processor, add the butter and puree until smooth. Transfer the purée to a medium saucepan with a spatula, stirring constantly over medium heat until the water evaporates and the purée thickens (about 5 minutes). Cool. Measure out 1 cup (well packed) of squash puree (reserve the rest for another use).

At the same time, bake the potatoes with the skins on the same baking sheet. About 1 hour or until potatoes are tender. Let cool and peel. While the potato is still hot, put it in a medium bowl with a potato masher and let it cool completely. Measure out 2 cups (uncompacted) of squeezed potato (reserve the rest for another use).

In a large bowl, combine squash, potato, 12 cups Parmesan cheese, egg, nutmeg and salt. Gradually add 1 34 cups of flour, kneading the dough directly into the bowl until it holds together. If the dough is very sticky, add more flour one tablespoon at a time. Transfer the dough to a floured surface, knead gently until the dough is smooth. Divide the dough into 8 equal pieces.

Prepare 2 large parchment paper-lined baking sheets with flour. Working with one piece of dough at a time, roll out on a lightly floured surface into a rope about 12 inches thick. Cut the rope into 34 inch pieces. Roll out one piece at a time on a gnocchi board on the baking sheets. Repeat with remaining dough. Cover dough with plastic wrap, being careful not to crush gnocchi. Chill for at least 1 hour. Can be made ahead of time (6 hours earlier). Keep in a cool place.

Cook gnocchi in a large pot of salted water until tender. 15-17 minutes (gnocchi will rise to the surface, but may rise to the surface before being fully cooked). Using a slotted spoon or spider, transfer gnocchi to the same baking sheets. Cool. Can be made ahead of time (8 hours earlier). Cover without crushing.

Heat a cast iron or non-stick skillet and melt the butter and add 1 tablespoon of olive oil. Add the sage and cook for 1 minute. Add the gnocchi, cook until golden brown, about 5 to 7 minutes. Season with salt and pepper. Transfer to a bowl. Sprinkle with remaining Parmesan cheese.