Preheat your oven to 400°F (200°C).

Toss the cubed butternut squash with olive oil, salt, and black pepper on a baking sheet.

Add the head of garlic (wrapped in aluminum foil) to the baking sheet and roast everything in the oven for 25-30 minutes, or until the squash is tender and caramelized.

While the squash is roasting, cook the pasta according to package instructions until al dente. Drain and set aside.

Once the squash is done, remove it and the garlic from the oven. Squeeze the roasted garlic out of its skins into a blender or food processor.

Add the roasted butternut squash, vegetable broth, heavy cream, dried thyme, nutmeg, and half of the grated Parmesan cheese to the blender. Blend until smooth and creamy.

In a large skillet over medium heat, combine the creamy butternut squash sauce with the cooked pasta. Stir until the pasta is evenly coated.

Serve immediately, garnished with the remaining Parmesan cheese and chopped parsley.