Preliminary Note: This cookie dough needs to chill for at least 3 hours, but I recommend chilling it overnight. The colder the dough, the thicker the cookies.
In a large bowl, use a hand-held or stand mixer with a paddle attachment to beat the softened butter, granulated sugar, and brown sugar on medium-high speed until the mixture is light and fluffy, about 2-3 minutes. Add the egg and vanilla extract, then beat on high speed until everything is fully combined. Scrape the sides and bottom of the bowl as needed.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt. With the mixer running on low speed, slowly add the dry ingredients to the wet mixture. Beat on low until just combined. The cookie dough will be thick. Switch to high speed and mix in the milk, followed by the chocolate chips. The dough will be sticky and tacky. Cover the dough tightly and refrigerate for at least 3 hours, or up to 3 days. Chilling the dough is essential for the best results.
When ready to bake, remove the dough from the refrigerator and let it sit at room temperature for about 10 minutes. If it’s been chilling for more than 3 hours, allow it to sit for about 20 minutes to make it easier to scoop and roll.
Preheat the oven to 350°F (177°C) and line large baking sheets with parchment paper or silicone baking mats. (This is recommended for all cookies.) Set the baking sheets aside.
Scoop and roll the dough into balls, about 1.5 tablespoons (35-40g) each, using a medium cookie scoop. For thicker cookies, make the balls taller than they are wide (almost like a cylinder or column). Place them 2-3 inches apart on the prepared baking sheets. The dough is sticky, so be sure to wipe your hands clean after shaping each batch of dough.
Bake the cookies for 11-12 minutes, or until the edges are set and the centers look slightly soft. Tip: If the cookies aren’t spreading much by the 9-minute mark, remove them from the oven and gently bang the baking sheet on the counter 2-3 times. This will help initiate the spread. Return the baking sheet to the oven to finish baking.
Let the cookies cool on the baking sheet for 5 minutes. During this time, you can press a few additional chocolate chips into the tops of the warm cookies if you’d like (this is optional, just for aesthetics). Then transfer the cookies to a cooling rack to cool completely. The cookies will slightly deflate as they cool.
Store any leftover cookies in an airtight container at room temperature for up to 1 week.