Preheat your oven to 400°F (200°C). Place the cubed butternut squash on a baking sheet, drizzle with olive oil, and sprinkle with salt. Roast for 25-30 minutes or until tender. Let cool slightly.

In a large bowl, mash the roasted butternut squash until smooth. Add the egg, 1 cup of flour, salt, black pepper, nutmeg, and 1/4 cup of grated Parmesan cheese. Mix until a dough forms. If the dough is too sticky, add more flour, a tablespoon at a time.

On a floured surface, divide the dough into four portions. Roll each portion into a long rope about 1/2 inch thick. Cut the ropes into 1-inch pieces to form dumplings.

Bring a large pot of salted water to a boil. Carefully drop the dumplings into the boiling water in batches. Cook for about 3-4 minutes or until they float to the surface. Remove with a slotted spoon and set aside.

In a large skillet, melt the butter over medium heat. Add the sage leaves and cook for 2-3 minutes until the butter is golden brown and the sage is crispy. Remove from heat.

Add the cooked dumplings to the skillet and gently toss to coat in the sage brown butter. Serve immediately with additional grated Parmesan cheese if desired.