Set a cast iron grill pan or griddle over high htat and let it get nice and hot. Put the peppers on their sides on the hot surface.
Cook, using tongs to rotate and position each one so that all side and the top and bottom get charred, about 20-25 minutes.
Put the peppers in a medium bowl and cover it tightly with plastic wrap. Let the peppers steam just until they're cool enough to handle, about 20 minutes.
Remove and discard the plastic wrap. Working over another bowl, cut or pull off pepper stems(which should come away with the cluster of seeds) and discard.
Tip the opening of the peppers toward the bowl and let any liquid inside pour out. Fish out and discard any seeds in the liquid. Cut the peppers lengthwise in half on a cutting board and trim off all the pale bits inside.
Cut the peppers lenghthwise in half on a cutting board, and wipe out the seeds. Turn the halves skin side up an;d scrape off the skin with the back of your knife or peel it with your fingers.
Tear the pepper pieces into irregular strips and add them to the bowl with the pepper juice. Add the garlic and vinegar, then massage the peppers with your hands, stirring and tossing them a bit. Stir it again and with your hands, tossing and rubbing the peppers, until the liquid looks creamy and a little viscous. Tear the basil leaves into big pieces andd stir them inches.
Eat the peppers right away, when they're still a bit warm, or up to an hour or two later. You can also deep them covered in the fridge for up to 2 days. Let them come to room temperature before serving.