Toss butter, brown sugar, and granulated sugar in a big bowl. Whip everything at medium-high mixer speed until light and fluffy (about 2 to 3 minutes.
Crack in the egg and pour in the vanilla. Turn the mixer speed to high until everything is nicely mixed together.
In another bowl, mix the flour, baking soda, cocoa powder, and salt until combined. With your mixer running low speed, slowly pour the dry ingredients into the wet ones (from Step 2) until the dough turns pretty thick.
Increase the speed again and add the milk and dark chocolate chips. Cover the sticky dough and pop it in the fridge for 3 hours to 3 days.
Take the dough out of the fridge and let it sit for about 10 minutes at room temperature (or 20 minutes if it's been chilling for over 3 hours). Preheat your oven to 350°F. Line your baking sheets with silicone mats or parchment paper.
Scoop about 1 ½ tablespoons of dough and roll it into a ball. Keep going until all the dough is used up. Make those dough balls much taller than they're wide. Space them on your baking sheets with 2 to 3 inches in between.
Bake them up for 10 to 12 minutes until the edges look set (but the center parts still have some softness to them.)
Let them chill on your baking sheet (out of the oven) for about 5 minutes. Add dark or white chocolate chips (optional) on top to make them look extra pretty. Then, transfer them over to a wire rack to chill completely.