In the bowl of a stand mixer with the paddle attachment or other large bowl with a handheld mixer, beat the vegan butter and sugar together until creamy, about 2 minutes.
Add the pumpkin puree and vanilla and mix until combined, scraping the sides and bottom of the bowl as needed.
Stop the mixer and add the flour. Sprinkle the cornstarch, baking soda, salt, cinnamon and pumpkin pie spice on top of the flour. Turn the mixer on low speed and mix until just combined. Scrape the bottom and sides to make sure everything is well combined.
Fold in the chocolate chips to incorporate.
Cover the bowl and chill the cookie dough in the refrigerator for 1 hour. If you skip this step, the cookies won't be very chewy. So chill if you can!
Preheat the oven to 350 degrees F and line two cookie sheets with parchment paper.
With a cookie scoop or spoon, scoop the dough and place on the prepared cookie sheets. Flatten the cookies with your hands, as they won't spread very much as they bake. Place a few more chocolate chips on top of each cookie, if desired.
Bake for 11-13 minutes until lightly golden on the edges. They will look soft and a little puffy but will get chewy as they cool. Do not over bake. Let them cool for 5 minutes on the pan before transferring to a cooling rack. Enjoy!