Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large mixing bowl, cream together the butter, margarine, brown sugar, granulated sugar, and powdered sugar until light and fluffy.
Mix in the egg until fully incorporated.
Add the squeezed pumpkin puree and vanilla extract to the mixture, and blend until smooth.
In a separate bowl, whisk together the cake flour, cornstarch, baking soda, baking powder, cream of tartar, salt, pumpkin pie spice, and ground cinnamon.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Be careful not to overmix to ensure the cookies stay tender.
Using an ice cream scoop/spoon, portion the dough into 12 even-sized balls and place them on the prepared baking sheet.
Because these cookies don’t spread much during baking, gently flatten each ball of dough slightly with your hand or the back of a spoon.
Bake in the preheated oven for 14 minutes, or until the edges are set and the tops are slightly golden.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.