Prepare the Croissant Bread Pudding: Preheat oven to 350°F (175°C). Butter a 9″ x 13″ baking dish and fill it snugly with the croissants.
In a medium saucepan, combine brown sugars and water over medium-high heat. Stir until dissolved. Meanwhile, warm heavy cream and half & half in a microwave-safe bowl.
Add rum and banana liqueur to the cream mixture, then pour into the sugar mixture, whisking constantly.
Slowly pour the hot sugar mixture into the beaten eggs, whisking constantly. Pour the custard over the croissants and press them down to soak through.
Bake for 30-45 minutes or until golden and set.

Make the Bananas Foster Sauce: In a saucepan, combine sugar and water, heating over medium-high heat until the sugar melts and turns amber.
Add cold butter cubes, whisking continuously. Once melted, add cream, rum, banana liqueur, vanilla, and a pinch of salt. Let it thicken, then add sliced bananas.
Drizzle the sauce over the baked croissant bread pudding and serve.