Bring 6 quarts of water to a boil and add 2 tablespoons salt.
In a 12 to 14-inch saute pan, combine the olive oil, pepper flakes, and garlic and saute until the garlic is almost brown, about 5 minutes. Add the tomatoes and tomato sauce and bring to a simmer.
Cook the pasta according to the package directions, until tender yet al dente, about 6 minutes. Drain the pasta and add it to tomato mixture. Toss over high heat one minute. Divide among 4 heated bowls, shave bottarga over each bowl, sprinkle with bread crumbs, and serve immediately.
Preheat oven to 200 degrees F.
Cut the tomatoes in half lengthwise, squeeze out the seeds, and remove the membrane. In a small bowl, combine the sugar, oil, salt, and pepper and coat the tomatoes with mixture.
Place the tomatoes, cut side down, on a baking sheet lined with parchment paper and place in the oven. Cook for 2 hours, or until the tomatoes are very soft and have lost about half of their liquid.
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 until the carrot is quite soft, about 5 minutes more. Add the tomatoes and their juice and bring to a boil, stirring often. Lower the heat and simmer until as thick as hot cereal, about 30 minutes. Season with salt, to taste.
This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.
Yield: 4 cups