Add the squash into a medium-sized pot and cover with water. Cook until fork tender. Drain and retain 3/4 cup of the water. Return butternut squash to pot.
Add heavy cream, butter and the reserved ¾ cup of water to the pot and bring to a boil. Reduce to simmer and let cook for approximately 5 minutes.
Add to blender or use an immersion blender to puree until creamy and smooth. Add the nutmeg, kosher salt, and black pepper.
Prepare the fettuccine according to the package directions. Before straining, reserve about ¾ cup of the pasta water. Add the strained pasta and parmesan to the pureed squash mixture and stir until well coated. If you need to thin the sauce, add the reserved pasta water 1 tablespoon at a time.
Sprinkle nutmeg and parmesan on pasta before serving if desired.