Preheat oven to 350 degrees F and line baking sheet with parchment paper. Place the pumpkin puree in a small bowl and blot it down with several paper towels to remove excess moisture. Set aside.
In a medium bowl whisk together the flour, baking powder, baking soda, pumpkin spice and cinnamon.
In a large bowl, using a hand mixer or stand mixer, beat together the butter, brown sugar and granulated sugar until combined, about 2 minutes, scraping the bowl as needed.
Add in the egg, vanilla extract, milk and pumpkin puree and continue mixing for another minute.
Add the flour mixture and beat together until just combined, scraping down the sides of the bowl with a rubber spatula.
With a small ice cream scooper (about 1 1/2 tablespoon of dough) scoop and place on the prepared cookie sheet.
Bake cookies for 10 minutes and then let them cool for 5 minutes. Transfer to a cooling rack to cool completely.