In a stand mixer or large bowl, cream together the softened vegan butter, pumpkin puree, brown sugar, granulated sugar, and vanilla extract 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. Avoid over-mixing.
Cover the bowl and chill the dough in the refrigerator for 30 minutes or overnight. This chilling step is essential.
Preheat the oven to 350 °F (177 °C).
Scoop 2-inch balls of dough using a medium cookie scooper or a large spoon. Press each ball down into a disk shape, as the dough will not spread much during baking. Arrange the cookies a couple of inches apart on a parchment-lined baking sheet.
Bake on the center rack for 10-12 minutes. Allow the cookies to cool completely on the baking sheet.
For the cinnamon frosting, in a medium bowl, whip together the softened vegan butter, vanilla paste, cinnamon, pumpkin pie spice, brown sugar, and powdered sugar until smooth and fully combined. If preparing ahead, cover and refrigerate until needed.
Fill a piping bag fitted with Wilton Piping Tip #2A with frosting. Pipe the cinnamon frosting onto the cooled cookies in a swirl pattern, starting from the center and moving outward. Sprinkle a little pumpkin pie spice on top before serving. Enjoy!