01 - Set oven to 400°F and line a baking sheet with parchment paper. Spread squash cubes evenly and roast for 30–40 minutes until tender and caramelized.
02 - Place peeled, quartered potato in salted boiling water and simmer until fork-tender, approximately 15–20 minutes, then drain thoroughly.
03 - Pass the roasted squash and boiled potato through a potato ricer or mash until completely smooth. Spread on a tray to cool slightly.
04 - Transfer cooled mash to a large bowl. Incorporate Parmesan, salt, pepper, optional nutmeg, and the beaten egg, mixing gently to combine evenly.
05 - Gradually add flour, stirring just until a soft, slightly sticky dough forms. Use only as much flour as needed for workable dough consistency.
06 - Turn dough onto floured surface, divide into four portions, roll each into a rope about ¾ inch thick, and cut into 1-inch pieces. Optionally, roll each piece over the back of a fork to create ridges.
07 - Bring a large pot of salted water to a gentle boil. Cook gnocchi in batches until they float to the surface, about 2–3 minutes, then remove with a slotted spoon.
08 - Melt butter in a skillet over medium heat, add fresh sage leaves and cook until fragrant. Toss cooked gnocchi in sage butter to coat, then serve immediately garnished with additional Parmesan and fresh sage.