Bring a large pot of heavily salted water to a rolling boil. Cook rigatoni until 1 minute shy of al dente (about 10–11 minutes).

Dip a measuring cup into the pot to reserve 1/2 cup of starchy pasta water before draining. Drain the pasta and set aside.

Melt 4 tablespoons of butter in a large skillet or Dutch oven over medium heat. Swirl gently as it melts and begins to foam.

Add the whole fresh sage leaves to the foaming butter. Fry for 2–3 minutes until the leaves are crisp and the milk solids turn a rich amber brown with an intoxicating nutty fragrance. Immediately transfer half the crispy sage leaves to a paper towel for garnish.

Add minced garlic to the skillet and sauté for 30 seconds until fragrant, stirring constantly so it does not burn.

Whisk the pumpkin puree and vegetable broth into the skillet until smooth. Pour in the heavy cream, freshly grated nutmeg, kosher salt, and cracked black pepper. Simmer gently over medium-low heat for 4 minutes until warm and velvety.

Stir in the grated Parmesan until melted and glossy. Add the cooked rigatoni along with a splash of the reserved starchy pasta water. Toss vigorously for 1–2 minutes until the pumpkin sauce clings lovingly to every ridge of the pasta.

Divide into warm bowls. Crown with the reserved crispy sage leaves, toasted pine nuts, shaved Parmesan, and freshly cracked black pepper. Serve immediately.