Preheat oven to 350° F. Grease a 9x13-inch baking pan and set aside.

In a large mixing bowl, cream the butter and granulated sugar with an electric mixer on low speed. Add the egg and vanilla. Continue to mix on medium speed until thoroughly combined. Blend in the bananas. Scrape down the sides of the bowl with a rubber spatula and mix for one minute more.

In a separate bowl, combine the flour, baking powder, baking soda, and salt. Add the flour mixture to the banana mixture and mix well, scraping down the sides of the bowl once with a rubber spatula.

Divide the batter in half. Add cocoa powder to half of the batter and mix well. Spread the cocoa mixture into the prepared pan. Carefully spoon the plain batter on top of the cocoa batter and carefully spread it out, trying not to mix the two layers.

Bake for 25 minutes or until a toothpick inserted near the center tests clean. Remove to a wire rack to cool completely.

To serve, cut into bars.