With a rolling pin, roll the bun halves until flattened.
Place on a baking sheet and brush both sides of the buns with 2 tablespoons of the oil. Broil until golden brown, about 1 minute per side.
In a bowl, combine the tomatoes, olives, oregano or basil, ½ teaspoon salt, ¼ teaspoon pepper, and the remaining oil. Transfer the buns to a platter and spoon the tomatoes over the top.