Combine first three ingredients in a large bowl; mix well. Add banana, stirring well to combine. Lightly spoon flour into dry measuring cup and level with a knife.
Combine flour, cocoa, baking soda, and salt, stirring well with a whisk. Add flour mixture to sugar mixture alternately with 1/2 cup milk, beginning and ending with flour mixture; mix after each addition.
Spoon the batter into 24 muffin cups lined with paper liners. Bake for 20 minutes or until cupcakes spring back easily when touched lightly in the center. Allow to cool, and frost if desired.
To make frosting: Place the butter and peanut butter into a medium bowl, and beat with an electric mixer.
Gradually mix in the sugar, and when it starts to get thick, incorporate milk one tablespoon at a time until all of the sugar is mixed in and the frosting is thick and spreadable. Beat for at least 3 minutes for it to get good and fluffy.