With an electric mixer, cream together butter, sugar, eggs, banana, and vanilla.
In a medium bowl, combine the flour, baking powder, soda, salt cinnamon and nutmeg. Stir into the wet ingredients until well-combined.
Cover dough and refrigerator for at least one hour. Drop tablespoons of chilled dough onto onto lightly greased baking sheets. Bake for 8-10 minutes, or until golden. Cool completely.
Meanwhile, beat together ingredients for frosting with an electric mixer. Gradually add the lemon juice until frosting reaches desired consistency.