12 ounces dried pasta, such as garganelli, gigli, campanelle, or gemelli
4 1/2 cups water
3 to 4 large garlic cloves, pressed or finely chopped
2 tablespoons olive oil
2 teaspoons kosher salt
Pinch red pepper flakes
1 cup pumpkin purée
1 cup heavy cream
1/2 cup grated Parmesan, plus more for garnish
Kosher salt and freshly ground black pepper, to taste
Freshly grated nutmeg, to garnish
For serving: Toasted pumpkin seeds, grated Parmesan, good-quality olive oil, or freshly chopped herbs, such as sage or parsley