Sprinkle the salt over the onion in a small bowl and set it aside.
Start the sauce by melting the butter in a large saucepan over medium heat. Add the onions and carrots and cook them, stirring, for 5 minutes. Add the sausage and cook, stirring, for 5 minutes, until the meat starts to stick to the bottom of the pan. Pour in the wine and scrape the bottom of the pan with a wooden or silicone spoon to deglaze it. When the alcohol in the wine has evaporated (you won’t smell it anymore), in 2 to 3 minutes, cover the pan, and reduce the heat to low. Cook the mixture for 20 minutes or until the wine is reduced to a sauce and the onion is so soft it is well combined with the cooked sausage.
Bring a large pot of salted water to a boil, then add the pasta. Cook it as the package directs to al dente.
While the water is boiling, heat vegetable oil in a saucepan on high heat. Fry the dried peppers for 20 to 30 seconds. Do not let the peppers burn or turn black.
When the pasta is cooked al dente, drain it and add it to the pan with the sauce. Stir the pasta and sauce together over low heat. Add the black pepper and pecorino, and stir them in for 1 to 2 minutes.
Divide the pasta and sauce between two bowls and top each with a fried pepper, additional pecorino cheese, and basil, if using.