Heat 2 tablespoons olive oil in a large skillet over medium heat. Add diced shallots and sauté for 3 minutes until translucent. Add minced garlic and cook for 1 minute until fragrant. Add cubed butternut squash, 1 teaspoon salt, 1/2 teaspoon black pepper, and nutmeg.

Pour in the broth and bring to a simmer. Cover and cook over medium-low heat for 12 to 14 minutes until the squash is completely fork-tender. Transfer the squash and broth to a high-speed blender, add heavy cream, and blend on high for 60 seconds until silky-smooth and velvety.

Bring a large pot of heavily salted water to a rolling boil. Cook the rigatoni according to package instructions until al dente (about 11-12 minutes). Reserve 1 cup of starchy pasta water before draining.

Wipe the skillet dry and set over medium heat. Melt 3 tablespoons of unsalted butter until foaming. Add fresh sage leaves in a single layer and fry for 2 to 3 minutes until dark green and crisp. Immediately remove crispy sage leaves with tongs onto a paper towel, leaving the nutty browned butter in the pan.

Pour the smooth butternut squash puree directly into the skillet with the fragrant brown butter over low heat. Stir in the freshly grated Parmigiano-Reggiano until fully melted and glossy.

Add the hot drained rigatoni to the skillet. Toss vigorously for 1 to 2 minutes so the velvety puree coats inside and outside every rigatoni ridge. Splash in 2 to 4 tablespoons of reserved pasta water as needed to create a glossy, clinging sauce.

Divide warm pasta into shallow bowls. Top generously with crispy fried sage leaves, extra shavings of parmesan cheese, and freshly cracked black pepper. Serve immediately.