Before cooking, slash the eggplant flesh a few times, sprinkle it with salt, and place in a colander for a half hour. Rinse and pat each one dry with a paper towel.
Put the olive oil in a nonstick skillet and let it get quite hot but not smoking. Fry the eggplants, cut side down, for 5 minutes, then drain and place in a shallow ovenproof dish. In the same pan, saute the onions and green or red pepper, adding extra oil if necessary. Cook until the vegetables have softened. Add the tomatoes, sugar, and seasoning and cook until the mixture is reduced, about 5 more minutes. Stir in the parsley.
Spoon this mixture on top of the eggplants. Bake, covered, in a 375-degree oven for 35 minutes or until completely tender. Cool, then chill thoroughly. Serve cold with a crusty French or Italian bread and an Italian white wine.