Cut the peppers in half, remove the seeds, ribs and stem. Slice into thin strips. Warm the olive oil in a wide, heavy-bottomed skillet using low heat. Add the onion and garlic and sauté until softened about 10 minutes. Add the pepper strips and continue to sauté another 5 minutes. Add the tomatoes, cover and cook over low heat stirring occasionally until the peppers are limp but still bright in color, another 20 minutes.
Remove from heat and add the basil. Serve hot or warm on crostini, baguettes, with goat cheese or a sprinkle of Parmigiano Reggiano.
Embellish it with olives, capers or finely sliced fennel. Serve on pizza or pasta.