Pour 2 tablespoons of olive oil on a baking sheet and place the peppers, cut side up on the oil. Turn the peppers over, season them with salt and pepper, and roast in the oven for 20 minutes. Place the warm peppers in a bowl, and cover with plastic wrap. Set aside to cool for at least 30 minutes.
For the basil oil, put the basil, 1 1/2 cups olive oil, and the garlic in the bowl of a food processor fitted with a steel blade. Pulse 6 to 8 times until the basil is finely chopped.
When the peppers are cool, remove and discard the skins. Slice the peppers and arrange them on a plate. Pour the basil oil over the peppers, and garnish with the basil leaves