Step 1Roast peppers on baking sheet at 400 degrees or over gas flame, turning with tongs, as necessary, until skin is charred and blistered on all sides, 10 to 15 minutes. Immediately place peppers in plastic bag and close tightly. Let charred peppers steam until cool, about 15 minutes. Using your fingers, slip off charred skins, then pull out and discard stem and seeds. Cut each pepper in half and trim away any tough white ribs. Cut into strips.
Step 2Oil interior of an 11x8-inch enamel, glass or earthenware dish and cover bottom with one-third of tomato slices.
Step 3Mince together parsley and basil and toss minced herbs and thyme together. Sprinkle one-fourth of herb mixture over tomatoes, plus salt and pepper to taste. Put layer of roasted pepper slices over seasoned tomatoes and again season these with minced herbs and salt and pepper. Continue layering until there are 3 layers of tomatoes separated by 2 layers of roasted pepper strips, with herbs, salt and pepper sprinkled on all but last layer of tomatoes. On this, sprinkle chopped capers and bread crumbs. Dribble 2 tablespoons oil over top. Bake at 400 degrees until top is crusty and tomatoes give off juices, 20 minutes. Cool at least 2 hours before serving.