Pour oil into 13x9x2-inch broilerproof ceramic baking dish. Add tomatoes; turn to coat with oil. Sprinkle with salt and pepper. Top with parsley and cheese. (Can be made 1 day ahead. Cover; chill.)
Preheat oven to 400°F. Bake tomatoes just until plump and shiny but not split, about 10 minutes.
Preheat broiler. Broil until tomatoes begin to split and cheese begins to color, about 2 minutes. Serve hot or warm.
