To make the caramelized bananas, melt the butter over medium heat in a small skillet. Add the bananas, brown sugar, bourbon, and cinnamon, and toss lightly until the bananas are evenly coated.
Sauté the banana mixture for 2 to 3 minutes, until the banana are lightly browned. Remove from the heat and set aside to cool.
To make the pancakes, mix the dry ingredients (flour, sugar, baking powder, baking soda, and salt) in a medium bowl.
Add the wet ingredients (buttermilk, egg, bourbon, melted butter, and vanilla) to the dry ingredients and mix until just combined (it can have some small lumps). See notes.
Preheat your skillet over medium heat and brush with butter or vegetable oil. Scoop about 1/4-cup of batter onto the hot skillet. Add 4 to 5 slices of banana to each pancake, lightly pressing them down.
Cook for 2 to 3 minutes, until small bubbles start to form on the surface. Flip, then reduce the heat to medium-low and cook on the other side for 1 to 2 minutes, until golden brown. Serve immediately.