Preheat oven to 375°.
Heat oil in Dutch oven over medium-high heat. Add eggplant and next 8 ingredients (eggplant through red pepper); saute 1 minute.
Add rice; saute 3 minutes. Stir in tomatoes and broth; bring to boil. Add cheese and chickpeas; stir well. Spoon rice mixture into a 13 x 9-inch baking dish. Cover and bake at 375° for 40 minutes or until rice is tender.