Cook the pasta according to package directions in salted boiling water. Reserve 1 cup of pasta water before draining, then set pasta aside.
In a large skillet over medium heat, melt the butter and add minced garlic. Sauté for about 1 minute until fragrant but not browned.
Stir in the pumpkin puree and cook for 2-3 minutes, stirring constantly to blend the flavors.
Pour in the heavy cream and whisk everything together until smooth and well combined.
Add the Parmesan cheese, nutmeg, sage, salt, pepper, and red pepper flakes if using. Stir until the cheese melts completely.
Let the sauce simmer on low heat for 5-7 minutes, stirring occasionally, until it thickens slightly.
Add the cooked pasta to the sauce and toss everything together. If the sauce seems too thick, add reserved pasta water a little at a time until you reach your desired consistency.
Taste and adjust seasonings as needed, then garnish with fresh parsley and extra Parmesan before serving.