Using a handheld or stand mixer, cream the butter on medium speed for about 20 seconds. Add the sugars with the mixer running on medium speed. Cream it all together until light and fluffy. Beat in the egg and vanilla. Scrape down the sides of the bowl as needed.
In a separate medium size bowl, toss the flour, cocoa powder, baking soda, and salt together. Slowly add to the wet ingredients with the mixer running on low. The dough will be very thick. By hand, stir in the milk, then fold in the white chocolate chips. The dough will be thick and very sticky. Chill for at least 2 hours and up to 36 hours, covered. Chilling is *mandatory.*
Preheat oven to 350F degrees. Line two large baking sheets with parchment paper or silicone baking mats. Set aside.
Take 2 Tablespoons of chilled dough and roll into a ball. Place on cookie sheet and press a few more white chocolate chips on the tops, if desired.
Bake for 12 minutes. Cookies will appear undone and very soft. Press down (gently) if cookies are too puffy. Allow to cool on the cookie sheet for at least 5 minutes before transferring to a wire rack to cool completely.
Cookies stay fresh and soft in an airtight container up to 7 days. Baked cookies and cookie dough balls freeze well for up to 3 months.