1. Preheat the oven to 350 degree F. Line eighteen 2 1/2-inch muffin cups with paper bake cups; set aside.
2. In a large bowl, beat the 1/2 cup butter with an electric mixer on medium speed for 30 seconds. Beat in granulated sugar until well mixed. Beat in eggs and the 1 cup mashed banana. Beat in flour and baking powder until combined. (The batter will be thick.) Spoon into prepared muffin cups.
3. Bake in the preheated oven for 18 to 20 minutes or until a wooden toothpick inserted in centers comes out clean.* Cool in muffin cups on wire rack for 10 minutes. Remove from muffin cups. Cool completely on wire rack.
4. For frosting, in a medium bowl, beat together powdered sugar, the 1/4 cup mashed banana, the 2 tablespoons butter, and the vanilla until smooth. Add several drops of yellow food coloring, if desired. Spread over cupcakes. Makes 18 cupcakes.