Yield: 9-inch pie plate
Preheat oven to 350 degrees F. Lightly butter 9-inch pie plate and set aside.
In a large bowl, add cubed bread, caramel chips, and sliced banana. In a large measuring cup, whisk together milk and eggs until smooth. Add vanilla, rum, sugar, brown sugar, and salt. Stir until sugar has dissolved. Pour liquid mixture over cubed bread. Toss to combine.
Transfer mixture (including all liquid) into prepared pie plate. Allow bread to soak for 10 minutes. Bake for 40-50 minutes until bread pudding has slightly puffed up, the liquid is set, and the top exposed bread pieces are toasted. Let bread pudding sit for 10 minutes to slightly cool. Serve bread pudding warm and dust with powdered sugar, if desired.