Bring 6 quarts of water to a boil and add 2 tablespoons of salt.
In a cold 12 to 14-inch saute pan, combine the olive oil, chile, and garlic and slowly sweat over medium heat until the garlic is soft, about 3 minutes. Add the sun-dried tomato, parsley, tomato sauce and 1 cup pasta cooking liquid and bring to a simmer.
Cook the pasta according to the package directions, until tender yet al dente, about 5 minutes. Drain the pasta and add it to the tomato mixture. Toss over high heat for 1 minute. Divide the pasta evenly among 4 heated bowls. Grate bottarga over each bowl like a dusting of cheese, sprinkle with bread crumbs, and serve immediately with a sprinkling of chili flakes and a drizzle of olive oil.
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 1 week in the refrigerator or up to 6 months in the freezer.