Slice & salt eggplant. Later rinse, pat dry and cut into ½ inch cubes. Coarsely chop or slice the vegetables. In a large stock pot or oven proof casserole, brown the onions & garlic in some olive oil. This will be the pot for the final assembled dish.
In a separate frying pan brown each of the vegetables separately in olive oil. When they are browned, add them to the first pot. Do not stir them together, try to keep the layers intact.
Add the fresh or canned tomatoes last. Add water to cover the vegetables if necessary. Season with thyme, bay leaves, rosemary, salt & pepper
Continue to cook over low heat if on stove top, or put in a 400 degree oven for at least 1 hr.