Bring a large pot of water to a boil and cook pasta according to directions on the package. In the 3 minutes, add the asparagus. Drain and set aside.
Meanwhile, in a pot, add chicken broth and butternut squash. If squash is not submerged, add water. Boil until butternut squash is easily pierced with a fork. Reserve 1 cup of broth and then drain the rest.
Transfer squash to a food processor and add 1/2 cup of broth and 1/2 cup milk. Process until everything is pureed.
Return to pot and add cheeses. Over medium heat, stir sauce until cheeses have melted. Season with salt and pepper. Pour over pasta and asparagus. Serve with a sprinkle of Parmesan, if desired.