Preheat the oven to 350℉ (177℃). Line baking sheet pans with silicone baking mats or parchment paper.
In a mixing bowl, whisk together the all-purpose flour, pumpkin pie spice, baking soda, baking powder, salt, and pumpkin pie spice. Set aside.
In a the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with a hand mixer, cream together the unsalted butter, light brown sugar, and granulated sugar until combined and smooth. Add in the pumpkin puree, egg, vegetable oil, and vanilla extract and mix until smooth.
Add in ⅓ of the flour mixture, mixing on low speed until mostly combined. Add in ½ of the milk and mix until mostly combined. Add another ⅓ of the flour mixture and mix, then the remaining milk, and the remaining ⅓ of the flour mixture, mixing in between each addition. Scrape the sides and bottom of the bowl and mix until the batter is smooth.
Portion the cookie batter using a large cookie scoop (3 tablespoons) and place on the prepared baking sheet pans. Bake the cookies for 11 to 12 minutes until the cookies are puffed up and the edges are set. Cool the cookies on the pan for 2 minutes and then transfer to a wire rack to cool completely.