Step 1: Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Step 2: Toss the cubed butternut squash with olive oil, salt, pepper, and nutmeg on the baking sheet until well coated.
Step 3: Roast the squash for 25-30 minutes, turning halfway through, until tender and caramelized at the edges.
Step 4: While the squash roasts, bring a large pot of salted water to a boil and cook the pasta according to package instructions until al dente.
Step 5: In a large skillet over medium heat, melt the butter. Once foaming, add the sage leaves and fry until they are crisp and the butter is browned. Remove the leaves and set aside.
Step 6: Transfer half of the roasted squash cubes to a bowl and mash them with a fork (or blend for a smoother texture), then stir the mash into the brown butter skillet.
Step 7: Add a ladle of pasta water to the skillet to create a creamy sauce, then toss in the cooked pasta and the remaining whole squash cubes.
Step 8: Stir in the grated cheese and adjust consistency with more pasta water if needed. Serve topped with the crispy sage leaves.