Preheat oven to 180 degrees C. Sift flour, baking powder, bicarb soda, salt and allspice together and set aside.
In a large bowl, cream the butter and sugar until light and fluffy. Add eggs and egg white and beat well. Add the mashed banana, vanilla and milk. Add the flour mixture and mix until well blended.
Divide batter into two 20cm pans. Bake in preheated oven for 25 to 30 minutes or until a toothpick inserted into the centre of the cake comes out clean. Cool completely and frost with cream cheese icing.