Boil the Rigatoni: Bring a large pot of water to a rolling boil. Season liberally with 1 tbsp coarse salt. Add rigatoni and cook until 1 minute shy of al dente according to package instructions (about 10 to 11 minutes). Before draining, carefully ladle out and reserve at least 1 cup of starchy pasta water. Drain pasta and set aside.

Crisp the Sage in Butter: While the pasta boils, melt 2 tbsp butter and 1 tbsp olive oil in a large deep skillet or Dutch oven over medium heat. Once sizzling, add the fresh whole sage leaves in a single layer. Fry for 2 to 3 minutes until crisp and slightly darkened, but not browned or burned. Transfer crispy sage leaves with a slotted spoon to a paper towel-lined plate to drain; sprinkle with a pinch of flaky salt.

Sauté Garlic & Build Sauce: In the same fragrant sage-infused butter, add the minced garlic and sauté over medium-low heat for 60 seconds until fragrant and golden. Whisk in the pumpkin puree, heavy cream, vegetable broth, ground nutmeg, optional cinnamon, salt, and black pepper. Whisk continuously until completely smooth and emulsified.

Simmer & Thicken: Bring the sauce to a gentle simmer over medium-low heat and let bubble gently for 3 to 4 minutes until slightly thickened and velvety. Stir in the remaining 1 tbsp butter and 1/2 cup grated Parmesan cheese until completely melted and glossy.

Toss & Emulsify Pasta: Add the drained al dente rigatoni directly into the warm skillet with the pumpkin sauce. Toss vigorously with tongs for 1 to 2 minutes so the sauce clings to every rib and fills the center of each pasta tube. If the sauce is too thick, splash in 2 to 4 tbsp of reserved starchy pasta water until it turns silky and glossy.

Garnish & Serve: Remove from heat. Divide into warm shallow pasta bowls. Crown each portion with the reserved crispy fried sage leaves, extra freshly grated Parmesan, and a generous pinch of cracked black pepper. Serve immediately while hot!