Preheat your oven to 350 degrees F, line a large baking sheet with parchment paper and set aside.
In a large bowl using a stand or hand mixer, cream together your butter, sugar, and brown sugar until fluffy. Then mix in your vanilla extract, pumpkin puree, and egg. Mix until smooth.
In a medium bowl whisk together your almond flour, coconut flour, baking powder, baking soda, and pumpkin spice until combined.
Slowly add your flour mix into your pumpkin puree mix, stir until combined. You should have a soft cookie dough.
Using a large cookie dough scoop, place your cookie dough ball onto your prepared baking sheet leaving at least 3 inches in between.
Bake for 15-18 minutes and allow to cool on the pan for at least 10 minutes before transferring to a wire rack to cool completely.
Frosting:
Once your cookies have completely cooled, make your frosting by whisking all of your frosting ingredients together until smooth.
Spread evenly onto the tops of each cookie and sprinkle with pumpkin spice, enjoy!