Add the cream, butter, squash and 3/4 cup water to a medium saucepan and bring to a boil. Reduce to a simmer and continue cooking until the squash is tender when poked with a fork, about 15 minutes. Puree using an immersion blender until super creamy and smooth, 3 to 5 minutes. Season with the nutmeg and 1 teaspoon salt.
Meanwhile, bring a large pot of salted water to a boil. Add the pasta and cook until al dente according to the package directions. Reserve 1/2 cup starchy pasta water and drain the pasta. Stir the pasta and Parmesan into the squash sauce and toss until well coated. Add the reserved pasta water 1 tablespoon at a time if needed to loosen the sauce. Serve with more Parmesan and grated nutmeg, if desired.