Preheat oven to 400°F (200°C). Spread cubed butternut squash on a large rimmed baking sheet. Drizzle with olive oil, salt, and pepper.

Drizzle exposed garlic head with olive oil, wrap tightly in foil, and place alongside squash on the baking sheet.

Roast for 25 to 30 minutes until squash is fork-tender with caramelized edges and garlic cloves are golden and buttery soft.

While roasting, melt butter in a large skillet over medium heat. Add fresh sage leaves and fry for 2 minutes until dark green and crisp. Remove sage to a paper towel; reserve infused butter in skillet.

Transfer roasted squash to a blender. Squeeze in roasted garlic cloves from skins. Add broth, heavy cream, nutmeg, salt, and pepper. Blend on high for 60 seconds until completely silky and smooth.

Cook pasta in a pot of generously salted boiling water until al dente (1 minute shy of package instructions). Reserve 1 cup of starchy pasta water before draining.

Pour blended squash puree into skillet with sage butter over medium-low heat. Stir in grated Parmesan.

Add drained pasta and ¼ to ½ cup pasta water, tossing vigorously for 2 minutes until glossy sauce clings tightly to pasta tubes. Garnish with crispy fried sage leaves and shaved Parmesan.