Toss eggplant slices with 3 tablespoon extra virgin olive oil, 1 tablespoon vinegar, oregano, 1/4 teaspoon salt and 1/4 teaspoon pepper. Lay eggplant slices on lightly oiled stoneware tray, overlapping just a little if needed, and let stand at room temperature for 15 minutes.
Preheat broiler. Broil eggplant on one side for 5 minutes, then remove from oven, flip eggplant, and top each slice with grated parmesan. Broil for another 4 to 5 minutes until golden brown and cooked through. Remove from oven and let tray cool to room temperature.
Toss arugula with sliced peppers, pine nuts, 1 tablespoon oil, 1 tablespoon vinegar and 1⁄4 tablespoon salt. Top eggplant with salad and serve directly from tray.