Preheat the broiler and move the rack down in the oven so that it isn't so close to the broiling elements.

Place the peppers on a baking pan. Broil the peppers, turning them occasionally so that they are charred on all sides. This may take around 20 minutes.

Transfer the cooked peppers to a plate, and cover with a bowl. Leave them to steam for 15 minutes. 

Place the peppers on a cutting board and remove the stalk and seeds. Flip the peppers over and use the edge of a knife to lift up the skin and remove as much as possible. Slice them into long strips about 1" wide.

In a large skillet, add the olive oil and garlic. Cook over a medium heat for a couple of minutes, then add the peppers. Stir to coat in the garlic oil, and season with salt and pepper.

Finally, stir in the shredded basil at the last minute, then serve.