Preheat oven to 350° F. Line baking sheet pans with parchment paper or silicone baking mats.
In the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with an electric hand mixer, cream together unsalted butter, granulated sugar, and light brown sugar for several minutes until light and creamy.
Add in egg and vanilla extract and mix on medium speed until the mixture is smooth.
In a separate mixing bowl, whisk together all-purpose flour, dark cocoa powder, baking soda, and salt.
Add in ⅓ of the flour mixture to the creamed butter and mix on low speed until just combined. Pour in ½ of the milk and mix on low speed until combined. Repeat this process with the next ⅓ flour mixture, ½ of the milk, and end with the remaining ⅓ flour mixture. Scrape the sides and bottom of the bowl and mix for a few seconds until everything is well combined and smooth.
Portion the cookie batter onto the prepared baking pans using a large cookie scoop. Allow space in between each cookie for spreading.
Bake the cookies for about 10-12 minutes until the cookies are puffed up and will bounce back when gently touched.
Remove from the oven. If the cookies are slightly misshapen, you can use the back of a spoon to gently press the sides of the cookies to create a round shape immediately when they come out of the oven. Allow the cookies to cool on the pan for a minute or two before transferring to a wire cooling rack to cool completely.