01 - Preheat oven to 400°F. Line a baking sheet with parchment paper. Toss the butternut squash cubes with a drizzle of olive oil. Spread evenly on the sheet and roast until tender and caramelized, 30 to 35 minutes.
02 - Boil the quartered potatoes in salted water until fork-tender, about 15 to 20 minutes. Drain thoroughly.
03 - Pass the roasted squash and boiled potatoes through a potato ricer or mash until smooth. Let cool slightly.
04 - In a large bowl, gently mix the mashed vegetables with the beaten egg, flour, Parmesan, salt, nutmeg, and black pepper until a soft dough forms.
05 - Turn dough onto a floured surface. Add more flour, one tablespoon at a time if sticky, avoiding overworking. Divide into four portions. Roll each into a rope approximately ¾ inch thick and cut into 1-inch pieces.
06 - Roll each piece over the back of a fork or a gnocchi board to create ridges if desired.
07 - Bring a large pot of salted water to a gentle boil. Cook gnocchi in batches. Once they float (2 to 3 minutes), cook one minute longer, then remove with a slotted spoon.
08 - Melt butter in a skillet over medium heat. Add sage leaves and cook until butter is golden and aromatic, about 2 to 3 minutes.
09 - Add cooked gnocchi to the skillet and toss gently to coat and warm through. Season with salt and pepper.
10 - Plate immediately, garnished with additional grated Parmesan and freshly ground black pepper.