In medium saucepan cook sweet peppers, onion, banana peppers, and garlic, in hot oil over medium heat 10 minutes, stirring occasionally. Carefully add broth and bring just to boiling; reduce heat. Boil mixture gently, uncovered, about 5 minutes or until it is reduced to 1-1/2 cups.
Cool pepper mixture slightly. Pour cooled mixture into a blender container; add lime juice and salt. Cover and blend until smooth. Press mixture through a sieve and discard solids. Return sauce to saucepan; heat through but do not boil. Makes about 1-1/3 cups sauce.