Preheat oven to 400°F (200°C). Toss cubed butternut squash, shallots, and whole garlic cloves with 2 tablespoons olive oil, kosher salt, black pepper, and nutmeg on a baking sheet.

Roast for 20 to 22 minutes until the squash cubes are caramelized at the edges and completely fork-tender.

Transfer roasted squash, shallots, and garlic into a high-speed blender. Pour in the warm vegetable broth and heavy cream. Puree on high for 60 to 90 seconds until a velvety, silky smooth golden sauce forms.

Bring a large pot of salted water to a rolling boil. Cook the rigatoni until al dente according to package directions (about 11 minutes). Reserve 1/2 cup starchy pasta cooking water before draining.

In a large deep skillet over medium heat, melt 3 tablespoons butter. Add the fresh sage leaves in a single layer and fry for 2 to 3 minutes until the butter foams, turns nutty brown, and the sage leaves become crisp and translucent. Immediately remove crispy sage leaves to a paper towel-lined plate.

Pour the velvety butternut squash puree directly into the skillet with the brown butter drippings over low heat. Whisk gently to combine.

Add the drained hot rigatoni and freshly grated Parmesan cheese directly into the skillet. Toss vigorously for 1 to 2 minutes, splashing in reserved pasta water as needed until the golden sauce clings luxuriously to every ridge of the pasta.

Transfer to serving bowls. Garnish with the crispy fried sage leaves, toasted chopped walnuts, freshly cracked black pepper, and an extra sprinkle of Parmesan. Serve hot.