Put the eggplant and zucchini in a colander and toss liberally with salt. Let stand for about an hour, if time allows, then rinse quickly and squeeze dry.
Put a wide flameproof casserole or deep skillet with a lid over medium heat. Add the olive oil and onions and cook, stirring occasionally, for about a minute; add the garlic, peppers, eggplant, and zucchini and cook, stirring to combine. Adjust the heat so the mixture simmers and cover. Cook, checking and stirring, for about 30 minutes, or until the vegetables are tender.
Add the tomatoes, stir, and re-cover. Cook for another 30 minutes, stirring occasionally, until the tomatoes have broken down and the vegetables are very soft. Taste and adjust the seasoning, stir in the basil, and serve hot or at room temperature.
