1. Heat the olive oil in a large saute pan and very gently cook the peppers and onion with some salt and pepper over a low heat for 40-45 minutes, stirring from time to time, until the peppers become very soft and the onion is dark golden.
2. About 10 minutes before the peppers will be ready, cook the spaghetti in a large pan of boiling salted water according to the packet instructions until al dente (tender, but firm to the bite). Stir the garlic into the peppers and cook for a few more minutes. Add the vinegar and check the seasoning.
3. Drain the pasta well and return to the pan. Tear in the basil, then add the pepper mixture and Parmesan. Toss well, then serve.
Tips: Peppers are often quickly stir-fried to be crunchy, but sometimes it's better to let gentle slow-cooking release their natural sweetness.