In a skillet set over medium heat, melt 6 tablespoons butter. Add brown sugar, maple syrup, and salt. Cook, stirring constantly for a few minutes until the mixture is smooth. If there are lumps in your sugar you might need to use a whisk. Once the mixture is smooth, remove from the heat and carefully stir in the bananas. Set aside and cool to room temperature while you prepare the French toast.
In a large bowl, whisk eggs, milk, half and half, brown sugar, cinnamon, and vanilla. Grease a 2 ½ or 3 quart casserole dish and place half the bread cubes in the bottom. Spoon half of the banana-brown sugar mixture over the bread. Top with the remaining bread cubes. Pour the custard (egg mixture) evenly over the bread cubes. Lightly press down on the top of the bread to allow the top layer of bread to absorb some of the custard mixture. Spoon the remaining banana-brown sugar mixture over the top of the French toast. Cover and refrigerate overnight.
Combine brown sugar, flour, cinnamon, and salt. Add butter, and using a spoon, work the butter into the dry ingredients until the butter is evenly distributed and the mixture resembles wet, clumpy sand.
Allow the casserole to cool for about 10 minutes before serving. This helps the custard to firm up and makes it easier to slice.
Dust the top of the casserole with powdered sugar and serve with warm maple syrup on the side. Optional garnishes include additional banana slices or chopped nuts for added texture and flavor.