Peel the eggplant and cut into lengthwise slices 3/8″ thick, about 3″ long and 1″ wide. Cut off the ends of the zucchini and cut into slices about the same size as the eggplant. Place the vegetables in a bowl and toss with 1 tsp. salt. Let stand for 30 mins. Drain & dry each slice in a towel.
One layer at a time, saute the eggplant and then the zucchini in 4 Tbsp. hot olive oil in a 10-12″ skillet for about a minute on each side to brown very lightly. Remove to a side dish.
In the same skillet, cook the onions and peppers (add additional olive oil if necessary) for about 10 mins., until tender but not browned. Stir in the garlic & season with salt & pepper to taste.
Slice tomato into 3/8″ strips. Lay them over the onions and peppers. Season with salt & pepper. Cover the skillet and cook over low heat for 5 mins. or until tomatoes have begun to render their juice. Uncover, taste the tomatoes with the juices, raise heat and boil for several minutes until juice has almost entirely evaporated.
Place a third of the tomato mixture in the bottom of a 2 & 1/2 quart casserole (about 2.5″ deep). Sprinkle 1 Tbsp. fresh, minced parsley over tomatoes. Arrange half of the eggplant and zucchini on top, then half the remaining tomatoes and parsley. Put in the rest of the eggplant and zucchini and finish with the remaining tomatoes and parsley.
Cover the casserole and simmer over low heat for 10 mins. Uncover, tip the casserole and baste with the rendered juices. Correct seasoning if necessary. Raise heat slightly and cook uncovered about 15 minutes more, basting several times, until juices have evaporated leaving a spoonful or two of flavored olive oil. Be careful of your heat; do not let the vegetables scorch in the bottom of the casserole!