Preheat the oven to 375 degrees F.
In a medium bowl whisk together almond and coconut flour plus pumpkin pie spice, baking soda, baking powder and salt.
In another small bowl whisk the egg with the pumpkin puree, maple syrup, melted coconut oil and vanilla extract.
Add the wet ingredients to the dry and mix until combined.
Use a cookie scoop or roughly 2 tbsp scoop to scoop the dough onto a parchment lined baking sheet. Use the back of a glass or mug to gently press the cookie dough down a little bit.
Bake for approximately 12 minutes, let cool and frost if desired. Store in an airtight container in the fridge for up to a week.
To make the frosting:
Place softened butter (very important that it's soft!), cream cheese and vanilla in a medium bowl (or bowl of a stand mixer).
Beat until well combined. Add powdered sugar and pumpkin pie spice and continue to beat on high speed until fluffy.
Spread frosting on cooled cookies and sprinkle with additional pumpkin pie spice