Cook pasta in a large pot of boiling salted water until al dente. Reserve 2 cups pasta water; drain pasta and set aside.
In pasta pot, heat oil over medium. Add rosemary and fry, stirring, until starting to brown, 1 to 2 minutes. Using a slotted spoon, transfer rosemary
to a paper towel, leaving oil in pot.
Carefully (oil is hot and will spatter) add pumpkin puree, garlic, half-and-half, Parmesan, vinegar, red-pepper flakes, and 1 cup reserved pasta water to pot. Stir sauce until heated through, 2 to 3 minutes.
Add pasta to sauce, and toss to coat. If sauce is too thick, add some reserved pasta water. Season generously with salt. Serve pasta sprinkled with fried rosemary and, if desired, more red-pepper flakes.
Frying rosemary in olive oil not only turns the herb into a crispy garnish -- it also infuses the oil to create a tasty base for the pumpkin sauce.