Preheat oven to 200 degrees C. Grease cookie sheets.
Sift the flour and baking powder, and set aside.
Using a mixer, beat butter and sugar until light and fluffy.
Add egg and vanilla extract, beat until combined.
Mix in the mashed bananas and slowly add the flour mixture. Don't over mix.
Stir in chocolate pieces and place the bowl in the refrigerator for 30 minutes to cool.
Using about a tablespoon of the mixture at a time, roll it into a ball, then place on the baking sheet.
Bake for 9-11 minutes or until edges are lightly browned.
Let cool, dust with powder sugar and serve with milk!