Heat the broiler. Cut the eggplant crosswise into 3/4-inch rounds and brush both sides with olive oil. Broil until light gold on each side, about 2 minutes per side. Let cool and cut into 1-inch pieces. In a medium Dutch oven, heat the 2 tablespoons olive oil over medium-high heat. Add the onion and bell pepper; saute until the onion is lightly browned, 12 to 15 minutes. During the last few minutes of browning, add the garlic, paprika, cumin, and cayenne. Stir in the tomato paste and cook, stirring, for 1 minute. Stir in 1/4 cup of the water and boil, using a wooden spoon to scrape up the juices from the bottom of the pan. Add the tomatoes, eggplant, chickpeas, remaining 1 cup water and salt. Bring to a boil and then simmer, covered, until the vegetables are quite tender, about 25 minutes, stirring once or twice. Stir in the parsley, adjust the seasonings, and serve.