In a medium bowl, beat together the butter and sugars until light and fluffy. Add in the egg and the vanilla, and cream together until fully combined.
In a separate bowl, mix together the flour, cocoa, baking soda and salt.
Slowly mix the dry ingredients into the wet ingredients until just combined. Add in the milk until fully incorporated. Fold in the white chocolate chips.
Cover the cookie dough, and place in the fridge for at least 2 hours to chill.
Preheat oven to 350°F. Line two baking sheets with parchment paper or silicone baking mats. Set aside.
Roll the cookies into balls, and place on the baking sheets around 1 inch apart.
Bake in the preheated oven for 12 minutes. Remove from the oven, and allow to cool on the baking sheets for 5 minutes before transferring to wire racks to cool completely.