Preheat the oven to 225 degrees and place a wire rack on a sheet pan.
In a large shallow bowl, whisk together the eggs, vanilla, cinnamon, and salt. Stir in the milk.
Heat the butter in a large skillet over medium heat. Meanwhile, soak the fingers in the egg mixture for at least 1 minute per side. Transfer the fingers to the skillet (you'll probably have to do two batches) and cook until golden brown on the bottom, about 3 minutes. Flip and continue to cook until the other side is golden, another 2-3 minutes.
Transfer the cooked fingers to the wire rack and place them in the oven to keep warm while the second batch is cooked.
Meanwhile, make the bananas. Melt butter in a skillet over medium heat. Place banana slices in skillet in a single layer. Cover with brown sugar.
Brown bananas on one side, then flip, allowing sugar to cook and the other side to brown.
Remove the skillet from heat then pour in bourbon. Let sizzle for a minute, then use the bourbon to slide banana slices out of skillet and onto a plate.
Serve the French toast warm with real maple syrup and the caramelized bananas.