Preheat oven to 350°F. Line 24 muffin tins with liners and set aside.
In a medium bowl, combine flour and baking powder. Set aside.
In the bowl of your mixer, beat butter, peanut butter and both sugars on medium speed for 2 minutes, until light and fluffy. Scrape down the sides of the bowl, then add eggs, one at a time, mixing well after each. Beat in vanilla extract.
With the mixer on medium low, beat in flour and milk alternately, starting and ending with the flour mixture. Scrape down the sides of the bowl and give the batter a good stir with a rubber spatula. Fold in chopped Butterfinger candy bars.
Fill prepared muffin tins 2/3 full and bake for about 20 minutes or until golden brown and tops spring back when lightly touched in the center. Let cool completely on wire rack before frosting.
In the bowl of your mixer, beat butter and peanut butter on medium speed until smooth. Add vanilla and milk, beating until combined.
With the mixer on low, slowly add powdered sugar, beating until just combined. Increase mixer speed to high and beat for one minute until smooth and fluffy.
Frost cupcakes generously and top with chopped Butterfinger bars.