Preheat the broiler, setting the rack about 6 inches from the heat. Meanwhile, cut out the stem ends of the tomatoes and cut each tomato crosswise into 3 or 4 slices, excluding the ends. Arrange in a large baking pan. Sprinkle with ¼ teaspoon of salt. In a bowl, stir together the breadcrumbs, cheese, oil, parsley, and thyme. Distribute evenly over the tomatoes.

Place on a rack 6 inches under the broiler. Broil until the crumbs turn golden brown, 2 to 3 minutes. Drizzle with olive oil, garnish with basil, and serve.