Remove egg from the refrigerator to come to room temp. To speed up the process, place egg in a bowl with warm water and set aside for 5 minutes.
Preheat oven to 350° degrees and line a baking sheet with parchment paper.
Melt butter and set aside to cool for a few minutes.
Combine the dry ingredients in a medium bowl: all-purpose flour, baking soda, baking powder, salt, pumpkin pie spice, sugars and whisk to combine.
In a large bowl- combine pumpkin puree, cooled melter butter, and egg. Whisk to combine.
Add dry ingredients to wet ingredients. Using a spatula or wooden spoon, gently combine but do not over mix. Batter is done when you see a few ribbons of flour.
Batter is thick and sticky. Spray a large ice cream scooper with oil and scoop batter onto pan, leaving 2-3 inches between each cookie as they puff up and spread sightly.
For a flatter, less domed cookie- spray the back of a spoon and gently press the batter out to thin.
Bake 10-12 minutes. They should spring back in the center when done. While cooling, make the icing.