Cut the core from each tomato. Cut each tomato crosswise in half. Arrange the halves, cut side up, on a rack and sprinkle with salt and pepper. Stud each tomato half with equal portions of the garlic slivers. Sprinkle with oil.
Place the tomatoes under the broiler and broil about 5 minutes, or until the garlic slivers start to burn. Discard the garlic slivers and sprinkle with chopped basil.