Begin by preheating oven to 350 degrees Fahrenheit.
Next in a large bowl, beat the 1 cup butter with an electric mixer until it is light and fluffy.
Add the sugar, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice to the bowl and beat until combined.
After that add the egg, vanilla extract, and pumpkin puree continue to beat until combined.
Lastly add in the flour and mix together well.
Scoop the cookie dough onto an un-greased baking sheet. (I was able to form 18 cookies, but you can form however many you want.)
Bake at 350 degrees for 11-12 minutes or until cookies are done.
Remove the cookies from the baking sheet and cool to room temperature on a baking rack.
For the frosting, beat together the ½ cup butter and 8 ounces cream cheese until light and fluffy. Add in the vanilla extract and powdered sugar and beat until well combined.
Frost the completely cooled cookies generously with the cream cheese frosting.