In a medium pan, melt butter, brown sugar, corn syrup and rum on stove over medium heat. Cook and stir until sugar is completely dissolved. Once sugar is dissolved, remove from heat and add vanilla and cinnamon.
Lightly grease a 9×13-inch baking pan.
Pour caramel sauce into prepared pan and make sure it is evenly distributed.
Place banana slices evenly over the sauce.
Layer and evenly sprinkle half of the croissant pieces over the bananas.
Evenly distribute the cream cheese cubes over the croissants.
Cover the top evenly with the remaining croissants.
In a medium bowl, combine eggs, milk, sugar, vanilla, cinnamon, nutmeg and pinch of salt and whisk together until completely smooth and well combined.
Pour the egg mixture over the bread.
Gently press the bread down with hands so that all of the bread can absorb the egg mixture.
Cover casserole and refrigerate overnight.
When ready to bake, remove pan from refrigerator and leave it out on the counter while oven preheats to 375 degrees F.
Bake uncovered for about 30-40 minutes.
Let it cool in pan 5-10 minutes.
Serve with fresh whipped cream to garnish.