Preheat oven to 350 degrees F. Grease an 8x8x2-inch baking pan; set pan aside. In a small bowl combine the flour, baking powder, soda, and salt; set aside.
In a medium mixing bowl beat butter with electric mixer on medium speed for 30 seconds. Add sugar, beating until combined. Beat in egg until well combined. Beat in banana and vanilla until combined. Alternately add flour mixture and buttermilk, beating on low speed after each addition just until combined. (Batter may appear slightly curdled.) Stir in chocolate pieces. Spread in prepared pan.
Bake for 25 to 30 minutes or until a wooden toothpick inserted near center comes out clean. Cool in pan on wire rack for 20 minutes. If desired, serve warm with fudge topping and banana slices. Makes 9 servings.