Place bell peppers directly over a gas flame and cook, turning with tongs, until charred all over.
Wrap each pepper in a paper towel, transfer to a bowl, and cover tightly with plastic wrap. Let stand until cool enough to handle, about 10 minutes, then rub off skins with a paper towel. Do not run peppers under water or you will wash away the flavor. Cut peppers into quarters and remove seeds and veins and discard.
Transfer to a bowl and toss with oil and vinegar. Season with salt and pepper. Add basil and toss gently to combine. Serve immediately or refrigerate, covered, up to 3 days. If refrigerating, bring to room temperature and wait until just before serving to add basil.