Drain pumpkin in a mesh sieve lined with cheesecloth for at least 1 hour. Press pumpkin down occasionally with the back of a spoon. Before using, squeeze cheesecloth to release most of the liquid. You should have 1/2 to 3/4 cup drained liquid. Whisk strained pumpkin, eggs, egg yolks, 1/2 cup of the Parmesan, Pecorino Romano, salt, and pepper. Set aside. Fill a large pot with water and bring to a boil. Meanwhile, cook bacon until crispy. Drain on paper towels and reserve bacon fat in pan. Cook pasta according to package directions. Before draining, reserve 1 cup pasta water. Drain pasta. Working quickly, whisk 1/4 cup hot pasta water into pumpkin/egg mixture to temper the eggs. Pour pasta back into hot pasta pot and add pumpkin mixture. Stir, using tongs, for several minutes, adding remaining pasta water as you go, until pasta is well-coated and cheese is melted. The sauce will become thick and creamy.Add 2 tablespoons of the warm reserved bacon fat and stir. Season with salt and pepper as needed. Top pasta with reserved bacon, remaining 1/2 cup Parmesan, and Italian parsley. Serve immediately.