Heat 1/2 cup olive oil in a large heavy skillet. Saute eggplant until each piece becomes saturated with oil. Use eggplant to line the bottom of a 3 quart casserole dish. Saute the red peppers until tender, and layer over eggplant in casserole dish. Top with mozzarella.
Heat remaining olive oil, and cook onions and garlic until lightly browned and caramelized. Stir in stewed tomatoes, basil, and oregano and simmer 5 minutes. Add balsamic vinegar, red wine vinegar, brown sugar, and tomato paste. Simmer for 10 minutes. Add anchovy filets and capers. Season with salt and pepper. Pour over the mozzarella cheese in the casserole dish. Sprinkle Parmesan cheese on top of sauce.
Bake in preheated oven for 20 to 25 minutes, or until cheese is melted.