In a large mixing bowl, toss the diced butternut squash with olive oil, salt, pepper, nutmeg, and cinnamon until well-coated.
Spread the seasoned butternut squash on a baking sheet in an even layer and roast for 25-30 minutes, or until tender and golden brown.
While the squash is roasting, cook the pasta according to package instructions until al dente. Drain and set aside.
In a large skillet over medium heat, sauté the minced garlic until fragrant, about 1 minute.
Add the roasted butternut squash to the skillet, along with the vegetable broth and heavy cream. Stir to combine and let it simmer for 5 minutes.
Using an immersion blender, blend the mixture until smooth. If you don’t have an immersion blender, you can carefully transfer the mixture to a regular blender and then return it to the skillet.
Stir in the grated Parmesan cheese until melted and well-combined. Adjust seasoning as needed.
Add the cooked pasta to the creamy sauce and toss until the pasta is well-coated.
Transfer the pasta mixture to a baking dish. Sprinkle the shredded mozzarella cheese on top.
Bake in the preheated oven for 15-20 minutes, or until the cheese is bubbly and golden.
Remove from the oven, garnish with fresh parsley, and serve warm.
Notes
For a lighter version, you can substitute half of the heavy cream with additional vegetable broth.