Preheat oven to 350º, line baking sheets with parchment paper.
In a large bowl, whisk together, flour, baking powder, soda, spices and salt.
In the bowl of an electric mixer, combine butter and sugars and beat for 1 -2 minutes until light and fluffy. Add pumpkin, egg and vanilla and beat until well mixed. Add flour mixture and beat until just combined.
Using a 11/2 tablespoon cookie scoop, drop dough onto prepared cookie sheets. Use your fingers dipped in flour to slightly flatten the tops.
Bake for 12-15 minutes, until the tops bounce back when lightly touched. Cool on wire rack.
For the frosting, combine butter and cream cheese in a medium bowl and mix with electric mixer until smooth. Add vanilla and powdered sugar and beat until well combined. It should be slightly thick. Spread on cooled cookies and sprinkle with pumpkin pie spice.