Preheat oven to 350° F. Prepare baking sheet pans with parchment paper or silicone baking mats.
In a large mixing bowl whisk together all-purpose flour, baking soda, baking powder, salt, and pumpkin pie spice. Set aside.
In a large mixing bowl or bowl of a stand mixer fitted with a paddle attachment, combine unsalted butter, granulated sugar, brown sugar. Cream on medium speed until combined.
Add in egg, vanilla extract, and pumpkin puree. Mix on low until combined.
Add half of the flour mixture to the pumpkin mixture and mix on low speed until most of the dry ingredients are combined.
Pour in milk and mix on low until combined and smooth.
Add the remaining half of the dry ingredients and mix on low until just combined. Scrape the bottom and sides of the bowl to ensure all of the ingredients are well incorporated.
Use a large (3 tbsp) cookie scoop or spoon and portion the batter onto the prepared baking sheet pans. Be sure to allow room between the cookies to account for spreading.
Bake for 13 minutes until the cookies have puffed up and are set.
Remove the pan from the oven and allow the cookies to cool on the pan for about 5 minutes. Transfer to a wire rack to cool completely.