Heat oven to 350°F; line sheets with parchment.
Whisk flour, pumpkin pie spice, baking powder, baking soda, cinnamon, and salt in medium bowl.
Cream butter and sugar in large bowl 2-3 minutes until light and fluffy.
Beat in pumpkin, egg, and vanilla thoroughly.
Gradually mix dry into wet on low just until combined.
Drop rounded tablespoons 2 inches apart on sheets.
Bake 13-15 minutes until cookies spring back lightly; cool completely on rack.
For frosting, beat cream cheese and butter smooth; gradually beat in powdered sugar and vanilla until creamy.
Spread or pipe onto cooled cookies; lightly dust with cinnamon.
Set frosting 10 minutes before serving or storing airtight.