Preheat oven to 375°. Cut squash in half and scoop out seeds and strings and discard. Drizzle inside of squash with olive oil and roast face down for 30 minutes or until squash is very tender and can be easily pierced with a butter knife.
During the last ten minutes of the squash roasting, begin boiling a pot of water for the pasta. Boil pasta according to package instructions. Drain and set aside.
Scoop squash into blender discarding skins. Add chicken broth to blender and mix until very smooth.
In a large pot, melt butter over medium high heat. Add garlic and cook for 30 seconds or until fragrant.
Add squash purée to pot with both cheeses and stir until melted together, about 2-3 minutes.
Lower heat to low and stir in cream, remaining salt and pepper until well mixed.
Add cooked noodles and stir until well coated with sauce. Serve hot! Top with additional salt and pepper to taste or minced rosemary.