Peel the eggplant if you like, then cut it into ½ inch cubes. Salt them liberally and place them in a colander for a half-hour or more. Rinse them thoroughly, then press between paper towels to remove as much moisture as possible.
Place the olive oil in a large non-stick skillet over medium heat. Add the eggplant, stirring and shaking almost constantly, until it absorbs all the oil and begins to brown and soften. Add the black pepper, onion, garlic, red pepper, and tomatoes, and continue to cook until all the vegetables soften and the mixture is thick, about 15 minutes; do not overcook -the vegetables should remain distinct.
Add the capers, sugar, and vinegar, parley, additional salt (probably not needed) and pepper. Remove from heat. Serve at room temperature.