1. Heat the oil in a large frying pan over medium heat. Add the peppers and stir frequently so they don’t stick and burn. After a few minutes, add the salt and pepper, sugar, and a spoonful of water and lower the heat. Continue to cook for a few minutes. When the peppers begin to be tender, taste one to see if you want to add more sugar or salt. Add the broth and cook the peppers until most of the broth is evaporated and the peppers are very tender and sweet and dark around some of the edges, about 20 minutes. Add more water from time to time if the pan is dry.

2. Meanwhile, bring a large saucepan of water to a boil. Stir in a small fistful of salt and the bucato. When the pasta is tender, reserve a cupful of the pasta water and drain the pasta quickly in a colander. Return the pasta to the pot you cooked it in and add the peppers and any liquid in the pan. Add ¼ cup of the reserved pasta water. Crush the Parmesan shavings between the palms of your hands over the pasta. Add the parsley and toss it all together over high heat for 1 minute. Add a little more pasta water if the pasta is sticky. Serve very hot. Pass the Parmesan.