Butternut Squash and Mascarpone Gnocchi

Trim stem and cut butternut squash in half lengthwise. Place in a microwave-safe dish, cover with plastic wrap, and microwave until tender, about 8 minutes. Transfer to paper towels to cool. Discard skin and set squash aside. Whisk mascarpone cheese, 1/2 cup Parmigiano-Reggiano cheese, eggs, salt, and black pepper in a bowl until smooth. Whisk in butternut squash until blended. Whisk in 1/2 cup flour until just incorporated. Whisk in remaining 1/2 cup flour, stirring until flour just disappears. Cover and refrigerate for at least 8 hours or overnight. Bring a large pot of salted water to a boil. Melt about 1/3 of the butter in large nonstick skillet; remove from heat. Scoop out approximately 1 1/2 teaspoons of the butternut squash dough with a spoon. Using a second spoon, push the dough off the first spoon and into the boiling water. Repeat with remaining dough, working in batches of 12 to 15 gnocchi at a time. When a gnocchi rise to the surface, cook for 1 additional minute, then transfer with a slotted spoon to the melted butter in the skillet. Place the skillet over medium-high heat; cook gnocchi until golden brown on one side, about 3 minutes. Season with cayenne pepper, salt, and black pepper. Turn gnocchi over and stir in sage leaves. Cook until second side is golden, 2 to 3 minutes. Transfer to plate and drizzle with browned butter from the skillet. Garnish with 1 tablespoon Parmigiano-Reggiano cheese and serve.