Heat broiler, with rack 6 inches from heat. Cut peppers in half through the stem; discard stems, ribs, and seeds. Place peppers cut side down on a rimmed baking sheet.
Roast peppers under the broiler until skins are charred, rotating baking sheet occasionally to cook evenly, about 10 minutes. Transfer peppers to a bowl, and cover with plastic wrap. Let steam until cool enough to handle, about 10 minutes.
Using a paper towel, rub peppers to remove blackened skin, and discard. Cut peppers into strips, and place in a clean bowl. Pour over strips any accumulated juice from other bowl. Add oil, vinegar, garlic, and basil; season with salt and pepper. Toss to combine. Serve warm or at room temperature.
The peppers can be stored in an airtight container in the refrigerator for up to one week.