Bring 6 quarts of water to a boil and add 2 tablespoons salt.
In a 12 to 14-inch saute pan, combine guanciale, garlic, onion and chili flakes and saute until onion is soft. Season with salt and pepper. Add tomato sauce, reduce heat and allow to simmer 10 to 15 minutes.
Cook bucatini according to package directions, until tender but still al dente, about 12 minutes. Remove pasta from heat, drain and add to simmering sauce. Toss to coat and divide among 4 heated bowls. Serve immediately, topped with freshly grated pecorino.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds one week in the refrigerator or up to six months in the freezer. Yield: 4 cups