Beat the softened butter in a large bowl or stand mixer until smooth and creamy, scraping the sides occasionally.
Add granulated sugar and packed brown sugar, beat for about 2 minutes until fluffy with no butter chunks.
Mix in peanut butter until well combined.
Add the egg and vanilla extract, and beat until incorporated, scraping the sides as needed.
In a separate bowl or on top of the flour, combine flour, baking soda, baking powder, and kosher salt, breaking up clumps.
Add the dry ingredients to the wet mixture and mix just until the dough starts to come together but some flour is still visible, then scrape bowl sides.
Gently fold in the chopped Butterfinger pieces until just incorporated.
Cover and chill the dough for at least 15 minutes to an hour for flavor development and easier handling.
Preheat the oven to 350°F and line baking sheets with parchment paper or silicone mats.
Shape dough into 2-inch balls and space them 1-2 inches apart on the prepared sheets.
Bake for about 10 minutes until edges are set and centers are no longer shiny.
Optionally, press cookies gently with a spatula to flatten slightly after baking for even spread.
Top cookies with extra Butterfinger crumbles if desired.
Let cookies set on the pan for at least 5 minutes, then transfer to a wire rack to cool completely.