TURN ON YOUR BROILER and adjust the rack to about 15 cm from the heat. In a large, heavy oven-proof skillet, heat the oil until hot and almost smoking. Add the breasts and saute them over medium heat until lightly browned on 1 side, about 3 minutes. Turn, season with salt and pepper, and place a slice of tomato with a piece of cheese on top of each cooked side of breast. Drizzle on the olive oil, season with black pepper and cook for about 1 minute. Transfer the pan to the broiler and cook until the cheese is hot and starts to melt slightly on top. Remove the pan, sprinkle on the basil, and serve at once.