Fill a large pot with water, add a generous pinch of salt, and bring to a boil. Cook the pasta until al dente, about 8 minutes, then drain and set aside.
While the pasta cooks, heat the olive oil in a large skillet over medium heat. Add the minced garlic and sauté for about 30 seconds until fragrant and just starting to turn golden.
Pour in the pumpkin puree and heavy cream, whisking together until smooth. Bring the mixture to a gentle simmer and cook for 3–4 minutes, allowing the flavors to meld and the sauce to thicken slightly.
Stir in the freshly grated Parmesan cheese, nutmeg, and season with salt and pepper. Continue cooking for about 2 minutes until the cheese melts and the sauce becomes silky and coats the back of a spoon.
If the sauce seems too thick, add a splash of the reserved pasta water and whisk until the sauce loosens to your desired consistency.
Transfer the cooked pasta into the skillet with the sauce. Toss gently to coat each piece evenly, allowing the flavors to meld for about 1 minute over low heat.
Remove from heat, let it sit for a minute to allow the sauce to settle and thicken slightly.
Serve hot, garnished with extra Parmesan cheese and a sprinkle of freshly ground black pepper if desired. Enjoy the comforting, velvety pumpkin Alfredo pasta!