Preheat oven to 350 degrees F. Line a baking sheet with a Silpat baking mat or parchment paper and set aside.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt. Set aside.
Using a stand mixer, cream the butter and peanut butter together until combined. Add the sugars and beat until creamy and smooth, about 3 minutes. Add in the egg and vanilla extract. Mix until combined.
With the mixer on low, slowly add in the dry ingredients. Mix until just combined. Stir in the chopped Butterfinger candy bars and milk chocolate chips.
Take about 2 tablespoons of dough and form a cookie dough ball. Place cookies on prepared baking sheet, about 2-inches apart. Slightly press down on the cookie balls with the palm of your hand.
Bake the cookies for 10 minutes or until they are golden at the edges and just set. Don’t over bake, the cookies will set up as they cool. Remove pan from oven and let cookies cool on the baking sheet for 4-5 minutes. Transfer to a cooling rack and cool completely.