In a large pot, bring 6 quarts of water to a rolling boil. Add a generous amount of salt. The pasta water should taste like sea water. Add the pasta to the pot and stir so it doesn’t stick to the bottom as it cooks. Cook the pasta according to package instructions, 8 to 10 minutes. Reserve some of the pasta cooking water. Drain the pasta in a colander and hold it there until the sauce is finished.
While the pasta is cooking, heat the oil in a large, high-sided skillet over medium heat until it shimmers. Add the sage sprigs and cook until crispy but not browned, about 1 minute. Transfer with a slotted spoon to a paper towel-lined plate and set aside. Fry the rosemary sprigs in the same hot oil until crispy but not browned, about 1 minute. Transfer to the same plate. Sprinkle the fried herbs with salt. Remove the leaves from the stems (discard the stems). Discard the oil or save for another use.
Return the skillet to medium heat and melt and cook 8 tablespoons (1 stick) of butter until it starts to turn light brown. Add the ginger and garlic and stir until fragrant, about 30 seconds. Add the pumpkin, sugar and some of the reserved pasta water. Stir in about 1/2 cup of Parmesan. Season with salt and pepper to taste. Stir in the remaining 2 tablespoons of butter. Add the cooked pasta to the skillet and warm gently, tossing to coat the pasta with the sauce. Stir in some of the fried sage and rosemary. Top with the remaining Parmesan and fried herbs.