Scoop out center and seeds of eggplant halves. Cut eggplants into 3/4 inch dice. Toss with salt in bowl and let it stand for at least 20 minutes. Drain off the fluid that collects, rinse well, and pat dry.
Heat olive oil in large saucepan over medium heat. Add onion, and saute until softened (about 5 minutes.) Add garlic, and cook 1 minute more, or until fragrant. Stir in tomatoes, chickpeas, and eggplants. Reduce heat to medium-low, and cook 15 minutes, or until eggplants are tender but not mushy.
Stir in capers and sugar, and cook 2 minutes more. Fold in parsley, and season with black pepper.