Preheat oven to 350 degrees F. Line a baking sheet pan with a silicone baking mat or parchment paper.
In the bowl of a stand mixer fitted with a paddle attachment or a large mixing bowl with an electric hand mixer, cream unsalted butter, brown sugar, and granulated sugar until light and fluffy. Scrape the sides and bottom of the bowl occasionally.
Add egg, vanilla extract, and pumpkin puree. Mix until well combined.
In a separate mixing bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, cinnamon, and pumpkin pie spice.
Add the flour mixture to the wet ingredients and mix on low speed until just combined. Again, scrape the sides and bottom of the bowl.
Turn the mixer to medium speed and mix the batter for about 30 seconds until the batter is well combined and smooth.
Portion the batter using a large cookie scoop (3 tablespoons) and place onto the prepared baking sheet pan. Allow room in between the cookies for spreading.
Bake the cookies for approximately 12 minutes. The cookies are done baking when they are puffed up and the cookies bounce back when gently touched on the top.
Remove the pan from the oven and allow the cookies to cool on the pan for a minute or two before transferring to a wire rack to cool completely.