Mix the flour, baking powder, cinnamon, ginger, nutmeg and allspice in a medium bowl, set aside.
Cream together the butter and sugars with an electric mixer. Add the egg and pumpkin puree and mix well, scraping the sides of the bowl as needed.
Mix in the flour on low speed, in three increments, until just combined. Scrape down the bowl as needed.
Refrigerate the dough for 30 minutes.
Preheat oven to 350°. Line cookie sheets with parchment paper or spray with cooking spray.
Roll out dough, on a lightly floured surface, to 1/4 inch thickness. Cut into shapes and place on prepared pans. Place pans in the freezer for 10 minutes.
Bake for 10-12 minutes or until cookies are set. Leave on the cookie sheet for 2 minutes, then move to a wire rack. Cool completely.