Using a cutting board, cut the eggplant into 2-inch cubes. Set aside. Core the sweet peppers, discarding the seeds and cut into 1 inch cubes.
In a large skillet, over medium-heat, heat the olive oil. Add the eggplant and cook until golden brown. Remove from the skillet and set aside.
Lower heat to medium-low and cook the peppers, onion, and garlic until they are tender, about 10 minutes.
Return the eggplant to the skillet, and add the tomatoes. Cook for 20 to 30 minutes, until the tomatoes have reduced down to a thick sauce.
Stir in the basil, salt, pepper, and garbanzo beans. Remove from heat and serve.