Cook pasta in a large pot of salted water until al dente. Drain and set aside, saving a little pasta water.
In a medium pot, heat oil over medium-low heat. Add shallots, garlic, and sage, and sauté until soft and fragrant (about 5 minutes).
Stir in coconut milk and pumpkin purée, whisking until smooth.
Add salt, black pepper, cayenne, nutmeg, and cinnamon. Taste and adjust salt and spices as needed. Keep the sauce warm on low heat.
Toss the pasta with the sauce, adding a splash of reserved pasta water if needed to loosen.
Taste again and adjust seasoning if needed.
Serve with grated Parmesan or Pecorino, crispy sage leaves, or garlic chips for garnish.