WET INGREDIENTS: Place the melted butter in a large bowl and allow it to fully cool to room temperature. This is very important or the cookies will end up greasy and spread. Once the butter is cooled to room temperature, add in the white and brown sugars. Whisk briskly until combined and smooth. Add in the pumpkin and the vanilla extract. Whisk again until combined.
DRY INGREDIENTS: In another bowl, stir together the flour (See Note 1), cornstarch, salt, baking soda, cinnamon, nutmeg, cloves, allspice, and pumpkin pie spice. Stir to combine.
COMBINE: Add all of the dry ingredients into the wet ingredients and mix until JUST combined. Do not over mix the dough.
FORM COOKIE BALLS: Roll tall cylindrical balls of dough that are 2 tablespoons in size. If you have a kitchen scale, the balls of dough should be about 45 grams. In a small bowl, stir together the cinnamon-sugar coating -- the white sugar, pumpkin pie spice, and cinnamon. Roll the balls of dough to coat them in the cinnamon-sugar mixture.
CHILL: Cover cookie balls with plastic wrap and place in the fridge for 1 hour. When cookie dough balls have almost finished chilling, preheat the oven to 325 degrees F.
BAKE: Place dough balls on a parchment or Silpat-lined sheet pan with plenty of space (I only add 6 cookie balls at a time) and bake for 10-14 minutes. Watch carefully, being sure to not over-bake. We like our cookies slightly under-baked best!
COOL: Remove from the oven and, working quickly, immediately press the edges of each cookie slightly inwards with the back of a spoon. Let stand on the cookie sheet for 5 minutes before removing to a cooling rack.
FROSTING: Meanwhile, prepare the frosting by beating the room-temperature butter and cream cheese until completely smooth. Mix in the pumpkin pie spice, vanilla, and salt. Add in the powdered sugar and then beat until the frosting is smooth. It will seem like you need more liquid, but just keep beating; it will come together!
DECORATE: Transfer the frosting to a plastic bag or piping bag and cut off the tip. Frost each cooled cookie by piping the frosting in a swirl on top. Sprinkle the tops of the cookies with leftover cinnamon-sugar mixture.