1. On a large tray, arrange a double layer of paper towels; top with a single layer of eggplant and zucchini; sprinkle with ½ teaspoon salt. Lay a double layer of paper towels over the vegetables and arrange a second layer of eggplant and zucchini slices; sprinkle with ½ teaspoon salt. Continue layering until all the vegetables have been salted. Top with a double layer of paper towels; place a tray on top and weight with a 5-pound bag of sugar or oilier heavy object. Let stand at least 1 hour.

2. Meanwhile, cook the lasagne noodles in plenty of boiling salted water until al dente, or firm to the bite; drain. Place noodles in a large bowl of cool water until ready to use.

3. Stir the ricotta, ¼ cup of the basil, 2 tablespoons of the Parmesan, and % teaspoon black pepper until blended; set aside.

4. Heat 2 tablespoons of the oil in a large skillet. Add the red and green bell peppers, onion, and garlic. Cook, covered, over low heat, stirring occasionally, until the peppers are tender, about 10 minutes. Uncover; sauté over medium-high heat until edges begin to brown, about 5 minutes. Stir in the com, black olives, and the remaiining ¼ cup basil. Season with salt and pepper; set aside.

5. When eggplant and zucchini are ready, wrap tightly in the paper towels and squeeze to extract as much moisture as possible. Heat 2 tablespoons of the oil in a large skillet over medium-high heat and fry as many vegetables as will comfortably fit in the skillet at one time, turning to brown evenly. Transfer to a tray lined with paper towels to absorb excess oil. Add additional oil to dry skillet, 2 tablespoons at a time, and heat before adding the zucchini and eggplant. Continue frying until all vegetables are browned.

6. Heat oven to 350°F. Select a 9 × 13-inch shallow baking dish. Spoon ½ cup of the chopped tomatoes onto the bottom of the dish. Lift the lasagne noodles individually from the water and blot dry on paper toweling. Arrange a single layer of 4 overlapping noodles on the bottom of the dish.

7. Top with a single layer of half the zucchini and the eggplant. Top with half tile pepper and com mixture. Sprinkle with 1 cup of the mozzarella and 2 tablespoons of the grated Parmesan.

8. Arrange a second layer of 4 lasagne noodles in a single overlapping layer. Spread with the ricotta mixture. Arrange a single layer of the remaining zucchini and eggplant slices; sprinkle with 1 cup of the mozzarella.

9. Arrange a third layer of the remaining 4 lasagne noodles in a single overlapping layer. Top with the remaining pepper mixture and the 1½ cups chopped tomato. Sprinkle with the remaining 2 cups mozzarella and 2 tablespoons grated Parmesan.

10. Bake until cheese is bubbly and edges browned, about 50 minutes. Let stand 15 minutes before cutting and serving.