Boil salted water and cook pasta until al dente; drain and toss gently with olive oil.
Meanwhile, melt butter in a pan over medium heat; sauté minced garlic until fragrant, about one minute.
Whisk in pumpkin purée and cream; simmer gently, then stir in Parmesan, nutmeg, salt, and pepper until smooth.
Combine pasta with the sauce over low heat; toss until the noodles are evenly coated and heated through.
Plate immediately, garnish with parsley, and serve warm.