Place the squash in a blender or food processor and add ½ cup of the vegetable broth. Puree until very smooth. Set aside.
Bring a large pot of water to a boil. Cook the pasta according to the package directions. Drain and return pasta to the empty pot.
In a medium saucepan, melt the butter over medium heat. Add the garlic and chopped sage and cook for 1 minute, stirring.
Whisk in the flour, nutmeg, salt and pepper. Cook for 30 seconds, stirring constantly.
Whisk in the remaining ½ cup of broth and the milk. Cook, stirring often, until thickened, about 3 minutes.
Remove from the heat and stir in the cheese. Then stir in the pureed squash mixture.
Stir the butternut cheese sauce into the pasta.
If the mac and cheese is not hot enough (this may be the case if the squash was cooled), warm it over low heat on the stove, stirring often, until hot. Serve.