Roast to Caramelized Tenderness: Preheat your oven to 400°F (200°C). Spread the cubed butternut squash and smashed garlic cloves on a large baking sheet. Toss with 2 tbsp olive oil, salt, and black pepper. Roast for 25 to 30 minutes, turning once halfway through, until edges are caramelized and squash is fork-tender.

Puree into Velvet: Transfer the roasted squash and garlic into a high-speed blender or food processor. Add the warm vegetable broth, heavy cream, and freshly grated nutmeg. Blend on high for 60 seconds until completely silky and velvety smooth. Set aside.

Fry Sage Leaves: Melt 6 tbsp unsalted butter in a large deep skillet over medium heat. Once the butter melts and begins to foam, add the dry sage leaves in a single layer. Fry for 1 to 2 minutes until the leaves become brittle and crackling crisp. Transfer the fried sage with a slotted spoon to a paper towel-lined plate.

Brown the Butter: Continue cooking the remaining butter in the skillet over medium-low heat for 2 to 3 minutes, swirling frequently, until milk solids turn a rich golden hazelnut brown and release a magnificent nutty aroma. Remove from heat immediately so it does not burn.

Boil Pasta: Bring a large pot of salted water to a rolling boil. Cook rigatoni until 1 minute shy of al dente (about 10 to 11 minutes). Ladle out and reserve 1 full cup of cloudy, starchy pasta water before draining.

Combine & Emulsify: Pour the pureed butternut squash sauce directly into the skillet with the brown butter over low heat. Add the drained hot rigatoni and 1/2 cup of reserved pasta water. Toss vigorously with tongs for 2 minutes to marry the sauce with the ridges of the pasta. Stir in grated Parmigiano-Reggiano until glossy and luscious (add more pasta water a tablespoon at a time if sauce is too thick).

Plate & Garnish: Divide into shallow warm pasta bowls. Top each with shattered crispy fried sage leaves, toasted chopped hazelnuts, shaved parmesan, and freshly cracked black pepper. Serve immediately while hot and creamy.