In a 10 to 12-inch saucepan, heat the oil until hot but not smoking. Add the onion and cook over medium heat, stirring often, until the onion just begins to turn golden. Add the pepper and continue stirring over medium heat until the peppers have softened, about 10 minutes, then add the chili flakes.
Stir in the pork, then add the wine. Add the tomato paste, tomato sauce and salt and pepper, to taste. Simmer for 20 minutes stirring occasionally.
In the meantime, in a large pot, bring 6-quarts water to a boil and add 2 tablespoons salt. Stir in the fusilli and cook according to the package directions, until al dente, but not too tender.
Drain the pasta, reserving 1cup of the pasta water. Add the fusilli to the saucepan with the pork ragu. Add a little pasta water, if needed, for moisture. Toss well to coat the pasta, and season, to taste. Divide evenly among 4 warmed pasta plates, sprinkle with the pecorino, drizzle with extra-virgin olive oil and serve immediately.
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.