Heat broiler on high.
Cut the eggplant crosswise into 1.5 – 2" cubes and brush both sides with olive oil. Broil until golden on each side. Let cool, and cut into 1" pieces.
In a deep saucepan, heat 2 tablespoons olive oil over medium heat.
Add the onion and saute for 2-3 minutes, until slightly wilted. Mix with the red onions, and cook for about 5-6 minutes. Add the red pepper, and sauté for one minute. Add garlic and all the spices and saute for another minute.
Pour the entire onion mixture into crock pot. Add both types of tomatoes, the eggplant, chickpeas, brown sugar and broth (just enough to cover vegetables).
Put on high and cook for about 3-4 hours. Add salt and pepper to taste.
Shortcut: To save a little time, you can throw everything in the pot and skip the first step of broiling the eggplant, but the extra flavor of broiling the eggplant first is well worth the effort.