Cook the pasta according to package instructions until al dente. Drain and set aside.
In a large skillet over medium heat, melt the butter. Add the minced garlic and cook until fragrant, about 1 minute.
Stir in the pumpkin puree and heavy cream. Bring to a simmer and cook for 3-4 minutes, stirring occasionally.
Add the grated Parmesan cheese and nutmeg to the sauce, stirring until the cheese is melted and the sauce is smooth.
Season the sauce with salt and pepper to taste.
Add the cooked pasta to the skillet and toss to coat in the sauce. Cook for an additional 2-3 minutes to heat through.
Serve the pasta warm, garnished with chopped parsley.