Wash the sweet peppers and remove the stem, seeds and internal white membrane, then cut into julienne strips. Heat the oil in a pan over medium heat and add the peeled and thinly sliced onion, the chili pepper and, after a minute, the peeled and chopped garlic.
Once the onion and the garlic have browned, add the sweet peppers, salt and black pepper and cook until the sweet peppers have almost disintegrated. In the meantime, cook the bucatini in a large pot of salted boiling water for the time indicated on the package.
Drain and dress the pasta with the prepared sauce and a few drops of the water in which the pasta cooked. Stir and garnish the dish with the Pecorino cheese, basil and a drizzle of olive oil.