Preheat the oven to 400 degrees Fahrenheit. Peel, seed, and cube the butternut squash.
Toss the squash cubes with the olive oil. Spread them in one layer on a baking sheet.
Roast for 25 to 30 minutes, until the squash is fork tender with lightly browned edges.
While the squash roasts, warm a drizzle of olive oil in a large skillet over medium heat. Cook the chopped onion for 5 to 7 minutes, until soft and translucent.
Add the minced garlic and cook 1 more minute, just until fragrant. Do not let it brown.
Add the roasted squash, the cooked onion and garlic, and the broth to a blender. Blend until completely smooth and creamy. You can also use an immersion blender in a large pot.
Pour the blended sauce into a saucepan and warm it over medium heat.
Stir in the milk, Parmesan, salt, pepper, and nutmeg. Simmer gently for 5 to 10 minutes, until slightly thickened.
Taste and adjust the seasoning. Add a splash of broth or reserved pasta water if the sauce is too thick.
Toss the sauce with cooked pasta such as penne, rigatoni, or fettuccine. Finish with extra Parmesan and fresh herbs.