Bring a large stockpot of water to a boil. Dice the shallots, mince the garlic, and pull 16 sage leaves from the stems, keeping 8 whole and finely chopping the other 8. Measure out all remaining ingredients and toast the pepitas in a small dry skillet over medium heat for 2 to 3 minutes until puffed and nutty.
Heat the olive oil and 1 tablespoon butter in a Dutch oven over medium heat. When the butter foams, fry the 8 whole sage leaves in a single layer for 30 to 45 seconds until crisp, then transfer to a paper towel lined plate and sprinkle with salt. Leave the flavored butter and oil in the pot.
Once the water is at a rolling boil, stir in 1 tablespoon kosher salt. Add the rigatoni, stir well, and cook according to package directions, usually 10 to 12 minutes, until just shy of al dente.
Return the Dutch oven to medium heat and add the remaining 3 tablespoons butter. Add the diced shallots and cook for 3 to 4 minutes until soft and translucent, then stir in the minced garlic and 8 chopped sage leaves and cook for 1 minute until fragrant.
Spoon in the entire can of pumpkin puree and stir to combine. Add the nutmeg, red pepper flakes, 1 teaspoon kosher salt, and black pepper, then cook for 2 to 3 minutes, stirring constantly, to deepen the flavor.
Reduce the heat to medium-low and slowly pour in the heavy cream while stirring. Simmer gently for 4 to 5 minutes until the sauce is smooth and slightly thickened, without letting it boil hard.
Before draining, scoop out at least 1 cup of the starchy pasta water. Drain the pasta in a colander and give it a quick shake, but do not rinse it.
Turn the heat to low and sprinkle the grated Parmesan into the sauce a handful at a time, stirring until melted and smooth. Add the drained pasta and toss with tongs until coated, then pour in the reserved pasta water about 1/4 cup at a time until the sauce is silky and loose enough to coat the pasta. Taste and adjust salt and pepper.
Divide the pasta among six warm bowls and top each serving with the crispy sage leaves, a spoonful of toasted pepitas, and extra grated Parmesan. Serve right away while the sauce is hot and creamy.