Whisk together almond flour, coconut flour, baking powder, pumpkin pie spice, baking soda, and salt in a large mixing bowl and set aside.
In the bowl of an electric stand mixer fitted with the paddle attachment, cream together butter and sugar until blended.
Mix in the egg, pumpkin, and vanilla extract. With the mixer set on low speed, slowly add the flour mixture and mix until combined.
Wrap the dough in plastic wrap and shape it into a round disk. Chill for a minimum of 2 hours, preferably overnight.
When ready to bake preheat the oven to 350 degrees F. Scoop the sugar cookies out using a small cookie scoop and place them on a silicone-lined baking sheet.
Bake for 9-11 minutes. Remove from the oven when the center is still slightly undercooked; it will finish baking as it cools.
Allow the cookies to cool 10 minutes on the baking sheet and transfer to a wire rack to cool completely.