Heat broiler to 500ºF. Cut the tomatoes crosswise in half and place them, cut-side up, on a broiling pan or shallow baking pan. Stick the garlic slivers into the tomatoes. Sprinkle with the rosemary, salt, and a few grinds of pepper. Drizzle with the oil. Broil about 3 inches from the heat for 10 to 15 minutes or just until the tomatoes release their juices and the garlic begins to brown. Spoon the pan juices over the tomatoes before serving. Serve as a side dish for breakfast, lunch, or dinner.
Unlike roasted tomatoes, broiled, grilled, and pan-broiled tomatoes get sweeter and maintain their shape because the cooking is so brief.