Preheat oven to 425°F (220°C). On a large rimmed baking sheet, toss the cubed butternut squash and garlic cloves with olive oil, salt, black pepper, and nutmeg. Spread in an even single layer. Roast for 18 to 20 minutes until tender and caramelized with golden-brown edges.

While squash roasts, bring a large pot of heavily salted water to a rolling boil. Cook the rigatoni until al dente according to package instructions (approx. 10 to 11 minutes). Before draining, ladle out 1/2 cup of starchy pasta water and set aside.

Transfer roasted squash and caramelized garlic into a high-speed blender. Add warm vegetable broth and heavy cream. Blend on high for 60 to 90 seconds until completely smooth, silky, and lustrous.

In a large deep skillet or Dutch oven over medium heat, melt the butter until foaming. Add fresh sage leaves in a single layer and fry for 45 to 60 seconds until delightfully crisp and aromatic. Remove sage with a slotted spoon to a paper towel, leaving the nutty browned butter in the skillet.

Pour the velvety squash puree into the skillet with browned butter over medium-low heat. Stir in grated Parmigiano-Reggiano until melted. Add drained rigatoni and toss vigorously for 2 minutes, splashing in reserved pasta water as needed until the sauce clings luxuriously to every ridge. Plate in warm bowls, top with crispy sage, toasted pine nuts, and extra shaved parmesan, and enjoy immediately.