Preheat an oven to 350 degrees F (175 degrees C). Grease a 9x13 inch baking pan.
Beat the butter and sugar with an electric mixer in a large bowl until light and fluffy. Add the egg and the vanilla and beat until well combined. Stir in the mashed banana, set aside.
Stir together the flour, baking soda, baking powder, and salt in a separate large bowl, and make a well in the center. Pour the banana mixture into the well and stir just until combined.
Remove half of the batter from the bowl. Mix the cocoa powder into the batter remaining in the bowl and stir well. Spread the cocoa batter in the bottom of the prepared pan. Spoon the remaining batter on top and use a knife to swirl the batter into a marbled design.
Bake in the preheated oven until the edges are golden, about 25 minutes. Allow to cool before cutting into 24 pieces.