Cook pasta 1 minute shy of the package instructions, then drain and set to the side.
Add the butternut squash cubes and chicken broth to a large pot, and bring to a boil on medium-high heat.
Reduce to a simmer, cover, and cook for 25 minutes until squash is tender.
Add in milk, garlic, sour cream, salt, ground mustard, and pepper.
Using an immersion blender (or move the mixture to a heat-safe high-speed blender) and puree until smooth.
Add in the cheddar and mozzarella, stirring until melted and creamy.
Fold in the shells and serve.