Preheat oven to 180 degrees C. Cut eggplant in half, scoop out the pulp, leaving a 1cm shell. Chop the flesh finely.
Heat 2 tablespoons olive oil in a frypan 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 breadcrumbs, 1/2 cup Gruyere, chopped olives, capers and lemon juice. Season with basil, chilli 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 tray.