Rinse the eggplants and cut lengthwise into thin slices. Pour the eggplant slices in a bowl and sprinkle with 2 tablespoons of salt. Fill the bowl with water. Let sit for about 30 minutes.
Rinse the zucchini and cut into slices. Rinse the tomatoes and cut into slices. Drain the mozzarella and cut into thin slices.
Remove the eggplant slices from the water and drain on paper towels. Pat the eggplant dry.
Heat 6 tablespoons of oil in a pan and saute the eggplant slices on both sides. Drain on paper towel and keep warm.
Saute the zucchini slices in 1-2 tablespoons of hot oil.
Season the vegetables with salt and pepper.
Grease a baking pan with olive oil. Alternately layer the eggplant slices, zucchini slices and tomato slices. Spread half of the mozzarella slices on the vegetables. Add the chopped tomatoes and drizzle with olive oil. Sprinkle with parmesan cheese. Spread the remaining mozzarella on top. Bake for about 30 minutes at 200°C (approximately 400°F). Remove from the oven, let cool and serve.