Preheat oven to 400°F (200°C). Line a large rimmed baking sheet with parchment paper. Toss cubed butternut squash and whole garlic cloves with 2 tablespoon olive oil, salt, and black pepper. Spread in a single layer and roast for 25 to 30 minutes until squash is tender and caramelized at the edges.

Bring a large pot of heavily salted water to a rolling boil. Cook rigatoni until just shy of al dente (about 1 to 2 minutes less than package instructions). Reserve ½ cup starchy pasta water before draining.

Transfer roasted squash and soft roasted garlic into a high-speed blender. Add 1 cup warm vegetable broth, heavy cream, and freshly grated nutmeg. Puree on high speed for 60 seconds until completely silky and velvety.

In a large deep skillet over medium heat, melt the butter. Add fresh sage leaves and fry for 2 to 3 minutes until butter turns nutty golden brown and sage leaves turn crisp. Remove fried sage with tongs and set aside on paper towels.

Pour the pureed squash sauce directly into the skillet with the fragrant brown butter. Stir over medium-low heat to warm through and emulsify.

Add the drained hot rigatoni and grated parmesan cheese into the skillet. Toss vigorously for 1 to 2 minutes, splashing in reserved pasta water as needed until the sauce clings luxuriously to every pasta tube.

Divide pasta among warm ceramic bowls. Garnish with crisp fried sage leaves, extra shaved parmesan, and coarse cracked black pepper. Serve hot.