1. Cut bananas in half crosswise; cut halves in half lengthwise.
2. Melt butter in a large skillet; stir in brown sugar and corn syrup. Bring to a boil over medium heat; stir in milk. Cook, stirring constantly, 1 minute. Remove from heat. Stir in vanilla and, if desired, rum. Add bananas, stirring just until bananas begin to soften. Remove from heat. Serve immediately.