Preheat the broiler. Arrange the peppers on a rimmed baking sheet and broil 2 inches from the heat for about 18 minutes, turning the peppers occasionally, until blistered and blackened all over. Let the peppers stand until cool enough to handle, about 20 minutes. Peel the peppers and discard the skins. Core and seed the peppers and cut them into 1/2-inch strips. Transfer the strips to a bowl and toss with diced smoked mozzarella, basil leaves and olive oil. Season with salt and pepper and serve.