Peel eggplant and cut into lengthwise slices 3/8 inch thick, about 3 inches long, and 1 inch wide. Scrub the zucchini, slice off the ends, and cut the zucchini into slices about the same size as the eggplant slices. Place the vegetables in a bowl and toss with the salt. Let stand for 30 minutes. Drain. Dry each slice with a towel. One layer at a time, sauté the eggplant, and then the zucchini in hot olive oil 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 slowly in olive oil for about 10 minutes, or until tender but not browned. Stir in the garlic and season to taste, with salt and pepper. Lay the tomato pulp over the onions and peppers. Cover the skillet and cook for about 5 minutes. Uncover, baste with juices and raise heat and boil for several minutes until the juices have almost entirely evaporated. Place 1/3 of the mixture in a 2 1/2 quart casserole and sprinkle over it 1 tablespoon of parsley. Arrange half the eggplant and zucchini on top, then half the remaining tomato mixture and another tablespoon of parsley. Put the remaining eggplant and zucchini over this and then finish with the tomato mixture and one tablespoon of parsley.