Preheat your oven to 350° F. Grease cookie sheets or line with parchment paper..
In a medium-sized bowl, whisk together the flour, baking soda, baking powder, pumpkin pie spice and salt. Set aside.
Using your mixer, cream the sugars and butter in a large bowl until combined well. Beat in the egg, pumpkin puree and vanilla until smooth. Beat in the flour mixture gradually at a medium speed.
Drop by tablespoon with a cookie scoop onto prepared baking sheets.
Bake for 15 to 18 minutes or until edges are firm (do not overbake). Cool on baking sheets for 2 minutes, then remove and cool on wire racks until completely cool.