Step 1: In a large mixing bowl, cream together the softened vegan butter, light brown sugar, and granulated sugar until light and fluffy. This can be done with an electric mixer or by hand.
Step 2: Beat in the pumpkin puree and vanilla extract until well combined and smooth. Scrape down the sides of the bowl as needed.
Step 3: In a separate medium bowl, whisk together the all-purpose flour, baking powder, pumpkin pie spice, cornstarch, and salt until thoroughly combined.
Step 4: Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed (if using an electric mixer) or by hand until just combined. Be careful not to overmix the dough.
Step 5: Cover the cookie dough and refrigerate for at least 1 hour. This chilling step is important for preventing the cookies from spreading too much during baking.
Step 6: Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper or silicone baking mats.
Step 7: Scoop rounded tablespoons of dough onto the prepared baking sheets, leaving about 2 inches between each cookie. Slightly flatten the tops of the dough mounds if desired.
Step 8: Bake for 10-12 minutes, or until the edges are lightly golden and the centers are set. Remove from the oven and let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
Step 9: While the cookies cool, prepare the frosting. In a medium bowl, cream together the softened vegan butter, vanilla extract, ground cinnamon, and optional pumpkin pie spice until smooth. Beat in the packed light brown sugar.
Step 10: Gradually add the powdered sugar, a half cup at a time, beating until the frosting is smooth and creamy. If the frosting is too thick, add a tiny bit of plant-based milk until it reaches your desired consistency. If too thin, add more powdered sugar.
Step 11: Once the cookies are completely cooled, generously spread or pipe the creamy cinnamon frosting onto each cookie. Enjoy immediately or store as directed.