Grease a 9"x13" baking dish with butter or cooking spray. Place cubed bread into the dish.
In a medium mixing bowl, add milk, half & half, eggs, egg yolks, vanilla, cinnamon, and sugar. Whisk to fully combine. Stir in mashed bananas.
Pour mixture over cubed bread. Allow to sit for 30 minutes.
Preheat oven to 350℉.
Bake banana bread pudding for 45-50 minutes or until center is fully cooked.
When the bread pudding is finished baking, add heavy cream, butter, brown sugar, and salt to a small sauce pan and place over medium heat. Stir while the ingredients come together and begin to boil. Let it gently boil for 1 minute or until thickened.
Serve the bread pudding then drizzle caramel sauce over it. Enjoy!