Cut eggplant into slices 1/2" thick, then cut slices into strips about 1" x 3". Quarter zucchini and then halve crosswise into 3" lengths. Place eggplant and zucchini strips in large bowl, sprinkle with salt and toss until covered. Let stand 30 minutes.
Place 2 TBS olive oil in large skillet and saute onion over low heat until just soft. Add diced red pepper and garlic and saute additional 5 minutes. Add chopped tomatoes and pepper and cook 5-8 minutes. Remove from heat.
Drain eggplant and zucchini, rinse well and dry thoroughly on paper towels. Coat in flour (do not use additional flour). Heat 3 TBS oil in large skillet and quickly saute eggplant and zucchini in small batches (adding more oil if necessary), and drain each batch on paper towels. Place 1/3 of tomato mixture in bottom of 12" skillet and sprinkle with 5-6 TBS grated cheese. In layers, add 1/2 vegetable mixture followed by 1/3 tomato, cheese, remaining vegetables, remaining tomato mixture and top with cheese. Cover and simmer gently for 10 minutes. Uncover pan and continue simmering 30-45 minutes or until most of the liquid has evaporated. Keep heat low to prevent scorching and check frequently. Serve hot or at room temperature. 6-8 servings.