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, dark cocoa powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with an electric hand mixer, cream the unsalted butter, light brown sugar, and granulated sugar until creamy. Add in the egg, vegetable oil, and vanilla extract.
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 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.