In a mixing bowl, cream butter and sugar. Add egg and vanilla extract; beat until thoroughly combined. Blend in the bananas.
Combine the flour, baking powder, baking soda and salt; add to creamed mixture and mix well. Divide batter in half. Add cocoa to half; spread into a greased 13 x 9-inch baking pan. Spoon remaining batter on top and swirl with a knife. Bake at 350F for 25 minutes or until the bars test done.
Yields about 2 Â½to 3 dozen bars.