Preheat oven to 350ºF.
Grease or spray a 13x9x2-inch pan.
With a mixer on medium speed, cream the butter and sugar together until fluffy.
Beat in the egg and vanilla extract.
Blend in the bananas.
Add the flour, baking powder, baking soda, and salt and mix well.
Divide the batter in half by removing about 1-1/2 cups of batter to another bowl.
Add the baking cocoa to one of the halves and mix it well.
Spread the chocolate batter into the prepared pan.
Spoon dollops of the white batter on top of the chocolate batter.
With a knife, swirl the white batter just a little into the chocolate batter.
Bake at 350ºF. for 25 minutes or until a cake tester inserted in the middle comes out clean.
Store cake covered on top of the counter.