In a large bowl, beat the 1 cup butter with anelectric mixer until light and fluffy.
Add the sugar, baking powder, baking soda, salt,cinnamon, and pumpkin pie spice; beat until combined.
Add the egg, vanilla extract, and pumpkin puree;beat until combined.
Add the flour; mix well.
Scoop the cookie dough onto an ungreased, parchment lined baking sheet to form 18 cookies. Bake at 350 for 11-12 minutes.
Remove the cookies from the baking sheet andcool to room temperature on a baking rack.
To make the frosting, beat together the ½ cupbutter and 8 ounces cream cheese until light and fluffy. Add the vanillaextract and powdered sugar and beat until well combined.
Frost the completely cooled cookies generouslywith the cream cheese frosting.