Preheat oven to 350 degrees F (175 degrees C). Cut eggplant in half, scoop out the pulp, leaving a 1/2 inch shell. Chop the flesh finely.
Heat 2 tablespoons olive oil in a skillet over medium heat. Cook chopped eggplant for about 1 minute. Stir in onion, garlic, and parsley, and cook until tender. Transfer to a large bowl, and mix in bread crumbs, 1/2 cup Gruyere, chopped olives, capers, and lemon juice. Season with basil, pepper flakes, salt, and pepper. Stuff into eggplant shells.
Top stuffed eggplants with overlapping slices of tomato. Sprinkle evenly with remaining 1/4 cup cheese, and drizzle with remaining 4 tablespoons olive oil. Place on baking sheet.
