Step 1: Preheat your oven to 400°F (200°C). Toss the cubed butternut squash with olive oil, salt, pepper, and nutmeg on a baking sheet. Roast for 20 minutes or until tender and slightly caramelized.
Step 2: While the squash is roasting, bring a large pot of salted water to a boil. Cook the pasta according to package directions until just al dente. Reserve at least 1/2 cup of pasta water before draining.
Step 3: In a large skillet or pan, melt the butter over medium heat. Continue cooking, stirring occasionally, until the butter stops foaming and turns a light brown color with a nutty aroma.
Step 4: Add the fresh sage leaves to the brown butter. Fry for about 30-60 seconds until they are crisp but not burnt. Remove from heat immediately if the butter darkens too quickly.
Step 5: Add the roasted squash and the cooked pasta to the skillet. Pour in the reserved pasta water and half of the Parmesan cheese.
Step 6: Toss everything together over low heat until a creamy sauce forms and coats the pasta. Serve immediately with the remaining Parmesan cheese and extra black pepper.