Cut vegetables into 1-inch cubes. Place in a colander, sprinkle lightly with salt, and set aside for 20 minutes.
Rinse eggplant and pat dry with a clean cloth or paper towels.
In a 4-quart pot, sauté onions and garlic in olive oil until onions are soft. Add eggplant and zucchini. Cook over medium heat for 5 minutes, stirring frequently.
Add all remaining ingredients. Cover and cook over medium-low heat for 30 minutes, stirring occasionally.
Remove cover. Cook 20 minutes, stirring frequently, or until most of the liquid has been reduced.