Preheat oven to 400°F (200°C). Toss cubed butternut squash on a parchment-lined baking sheet with 2 tablespoons olive oil, 1/2 tsp kosher salt, and black pepper. Spread into a single layer and roast for 25 to 30 minutes until edges are caramelized and caramelized fork-tender.

Bring a large pot of heavily salted water to a rolling boil. Add rigatoni and cook 1 minute short of al dente according to package instructions. Scoop out and reserve 1 cup of starchy pasta cooking water before draining.

While pasta boils, melt 2 tablespoons butter in a deep 12-inch skillet over medium heat. Add whole sage leaves and fry for 60 to 90 seconds until dark green and delightfully crisp. Use a fork to transfer crispy sage leaves to a paper towel-lined plate. In the same fragrant sage-infused butter, sauté sliced shallots and minced garlic for 2 minutes until soft and translucent.

Transfer roasted butternut squash, sautéed shallots, garlic, warm bone broth, heavy cream, freshly grated nutmeg, and remaining 1/2 tsp salt into a high-speed blender. Blend on high for 60 seconds until impossibly smooth, velvety, and glowing golden-orange.

Pour the velvety squash puree back into the large skillet over medium-low heat. Stir in freshly grated Parmigiano-Reggiano and fresh lemon juice until cheese is completely melted and emulsified.

Add the drained hot rigatoni into the simmering sauce. Pour in 1/2 cup of reserved starchy pasta water and toss vigorously with a wooden spoon for 2 minutes. The starch binds the cheese and squash puree, creating an ultra-glossy velvet emulsion that hugs every single pasta ridge.

Ladle into wide, warm shallow pasta bowls. Crown with the crispy fried sage leaves, toasted pumpkin seeds, shaved parmesan curls, and a generous crack of black pepper. Serve hot immediately!