With a sharp knife, cut off the stem and peel each eggplant lengthwise, leaving 4 evenly spaced 1 inch wide strips of peel intact. Slicing between the strips, cut each one in half. Cut side up, make three or four 4 inch long lengthwise slashes through the thickest part of each half, spacing the slashes about 1 inch apart. Sprinkle the eggplants with 1 tablespoon of the salt and arrange them in two or three layers in a large flat bowl or pan. Pour in enough cold water to cover them by 1 inch, weight with a heavy casserole, and let the eggplants rest at room temperature for at least 30 minutes.

Meanwhile, drop the onion rings into a large colander set in a deep plate. Sprinkle the onions with 3 tablespoons of the salt, turning them about with a spoon to coat them evenly. Let stand at room temperature for at least 30 minutes, then rinse the onions under warm running water and squeeze them gently but completely dry. Place them in a bowl, add the tomatoes and the remaining 2 teaspoons of salt and toss together thoroughly.

Pour 2 tablespoons of the oil into a heavy casserole large enough to hold the eggplants in one layer. Drain the eggplants, rinse them under cold water and pat dry with paper towels. Arrange the eggplants cut side up in the casserole. Force as much of the onion-tomato mixture as possible into the slashes and spread the rest on top. Place a garlic clove on each eggplant half, and sprinkle them with the remaining 6 tablespoons of oil. Pour in the cup of water and bring to a boil over high heat. Reduce the heat to low and simmer covered for 1 hour and 15 minutes, or until the eggplants are tender. Cool in the casserole to room temperature.

To serve, arrange the eggplants n a large platter or individual serving plates, spoon the cooking juices around them and sprinkle with parsley.