In a stand mixer or large bowl, cream together the softened butter, pumpkin puree, brown sugar, granulated sugar, and vanilla until the mixture is light and fluffy.

In a separate large bowl, whisk together the all-purpose flour, baking powder, pumpkin pie spice, cornstarch, and salt.

Gradually add the dry ingredients to the wet ingredients bowl, mixing on low speed until just combined. Do not over-mix.

Cover the bowl and place it in the fridge for 30 minutes or overnight.

Preheat the oven to 350 ?F (177 ?C).

Scoop 2-inch balls of dough out with a medium cookie scooper or a large spoon. Press down to flatten the dough balls into disks.

Arrange the disks a couple of inches apart on a parchment-lined baking sheet.

Bake on the center rack for 10-12 minutes. Let them cool down completely on the baking sheet.

For the frosting, in a medium bowl, whip together all the frosting ingredients until fully combined.

Spoon icing into a piping bag fitted with the Wilton Piping Tip #2A. Pipe the cinnamon frosting on top of the cooled cookies in a swirl, starting from the middle and moving outwards. Sprinkle pumpkin pie spice on top.