Bring a large pot of salted water to a boil and cook your pasta until just al dente. Before draining, scoop out about a cup of the starchy pasta water and set it aside. This water is liquid gold for loosening the sauce later, so don't skip this step.
While the pasta cooks, melt the butter with the olive oil in a skillet over medium heat. Add the chopped shallot and cook for about 3 minutes until soft. Stir in the garlic and sage, and cook for another minute until fragrant but not browned.
Stir the pumpkin puree straight into the skillet with the aromatics. Let it cook for 2 to 3 minutes, stirring often, so the raw edge cooks off and the pumpkin flavor deepens slightly before you add any liquid.
Pour in the heavy cream and about half of the reserved pasta water. Whisk everything together until smooth, then add the nutmeg, salt, and pepper. Let the sauce simmer gently for 5 minutes so the flavors come together.
Turn the heat to low and stir in the grated parmesan a little at a time until it melts completely into the sauce. If the sauce looks too thick, add more of the reserved pasta water until it reaches a silky, pourable consistency.
Add the drained pasta directly into the skillet and toss until every piece is coated in sauce. Let it sit for a minute off the heat so the pasta can soak up the flavor, then plate it up right away while it's warm.