To make sauce: In a small pan, melt butter and brown sugar over medium heat; carefully add bananas and simmer for 2 minutes. Remove from stove and add bourbon; return to flame and continue simmering an additional 2 minutes. Cover and keep warm until ready to use.
To make batter: In a large bowl, whisk eggs and salt. Add vanilla. Pour in cream, continuing to whisk until well blended.
Melt 1 to 2 tablespoons butter in a large frying pan over medium-high heat. Dip each bread slice in batter and cook each side until golden brown. Repeat with remaining bread slices.
Transfer 2 bread slices to individual plates and top with banana slices and sauce. Serve with maple syrup or powdered sugar.