Melt butter in a heavy bottomed skillet over medium heat. Once butter is melted add the brown sugar and pinch of cinnamon. Stir with a wooden spoon until the sugar melts into the butter and becomes a sauce. Add bananas and toss together. Let cook until the bananas are soft and incorporated into the sauce. Remove to a bowl and let cool completely. Once cool, add cream cheese and mash with a wooden spoon.
Using a paring knife, cut a 2-inch-long slits in 1 side of each bread slice, cutting 3/4 of way through bread and creating pocket that leaves 3 sides of bread intact. Divide banana mixture equally among the bread pockets.
In a large bowl, add eggs, heavy cream, milk, cinnamon and rum and whisk to combine. Pour mixture into a 13 by 9-inch casserole dish. Put the bread into the egg mixture and let soak for 3 minutes, turning occasionally. Remove the bread from egg mixture, using a spatula, letting the excess drain off.
Spray a wire rack with nonstick spray and put the rack on a baking sheet. Put the bread on the rack and transfer to the oven.
Bake the French toast until it is golden brown and filling is hot, about 25 minutes. Transfer the toast on a serving platter and garnish with confectioners' sugar and maple syrup.