Preheat broiler. Cut bell peppers in half lengthwise; discard seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Place eggplant halves, skin sides up, on baking sheet. Broil peppers and eggplant 15 minutes or until blackened. Place peppers in a zip-top plastic bag; seal. Let stand 10 minutes. Peel peppers. Scoop out eggplant pulp. Discard shells.
Combine 1 cup broth and onion in a medium saucepan; bring to a boil. Reduce heat; simmer 5 minutes. Add 2 cups broth, bell peppers, and eggplant pulp, and simmer 10 minutes. Place bell pepper mixture in a blender; process until smooth. Return pureed mixture to pan. Stir in basil, salt, and black pepper. Garnish with cilantro sprigs, if desired.