Step 1

Heat broiler. Broil peppers on a foil-lined rimmed baking sheet, turning with tongs every 5–7 minutes, until all sides are charred, about 20 minutes. Let sit until cool enough to handle.

Step 2

Peel peppers and discard skins. Tear flesh into ½"-wide strips. Transfer to a medium bowl and add basil sprigs, garlic, oil, salt, and any juices on baking sheet; toss to combine. Cover and let sit room temperature at least 1 hour.

Step 3

Top with basil leaves just before serving.Do ahead: Peppers can be marinated 3 days ahead. Chill if making more than 1 hour ahead. Bring to room temperature before serving.