Bring a pot of salted water to a boil. Cook pasta until al dente. Reserve 1 cup pasta water, then drain.
Heat olive oil and butter in the same pot. Add onion and garlic, sauté until soft and fragrant.
Stir in pumpkin purée and broth. Let it simmer for 2–3 minutes.
Add cream (or cream cheese) and whisk until smooth. Season with nutmeg, salt, pepper, and red pepper flakes.
Stir in Parmesan. Add pasta water as needed to loosen the sauce.
Toss cooked pasta in the sauce until coated. Top with sage and extra Parmesan. Serve warm.