Add brown sugar and softened butter to a medium mixing bowl and beat with the paddle attachment until combined and fluffy, about 1 minute. Add pumpkin puree, egg, vanilla, and beat for another minute until thoroughly combined.
In a small bowl, whisk together flour, baking soda, baking powder, salt, and pumpkin pie spice until evenly distributed. Add the flour mixture to the pumpkin mixture with the mixer on low speed, and mix until just combined.
Scrape the side and bottom of the bowl to ensure everything is well mixed. Allow the dough to rest in the refrigerator for at least 1 hour or overnight.
Take the dough out of the fridge and divide into 13 portions, about 1 1/2 oz each. For precise measurement, use a kitchen scale. Grease your hands with melted butter and roll the dough into balls. Set them on a parchment lined baking sheet about 2 inches apart. Place the baking sheet back into the refrigerator.
Preheat the oven to 375°Mix granulated sugar and pumpkin pie spice together for topping and set aside.
When the oven is ready, take a baking sheet with the cookie dough out of the fridge. Grease the bottom of a measuring cup with melted butter and flatten the dough balls. It may be a little sticky still, slide the measuring cup from side to side to remove it from the cookie dough instead of lifting straight up. Sprinkle the sugar mixture over each cookie generously and bake for 13 minutes.
Let the cookies cool on the baking sheet for 8 minutes. Press a Butterfinger skull into the middle of the slightly cooled cookies. Place the cookie tray in the freezer immediately to stop the candy from melting further.