Bring a pot of water to a boil and add butternut squash. Cook until squash is softened and drained. Place in a food processor, add broth, and pulse until mixture is smooth. Set aside.
Prepare pasta according to box (or how you normally do it!) Drain and set aside.
In a small pan, heat butter over medium-low heat until melted. Whisk in flour and let cook for 1-2 minutes. Whisk in milk, butternut squash, salt, pepper, and garlic. Continue to whisk until the mixture begins to thicken (1-2 more minutes). Once thickened, remove from the burner and mix in cheese, continuing to whisk until melted (if the sauce seems too thick, add a little more milk.) Stir into pasta and serve.