Combine flour, cocoa, sugar, baking soda, and salt in a food processor. Pulse several times to mix.
Cut the butter into 4 pieces and add to food processor. Pulse several times.
Combine the milk and vanilla and with processor running, add to mixture. Process until dough clumps together.
Remove dough from machine and knead several times so that it is evenly blended.
Shape the dough into a log about 1 ¾ inches wide and wrap in plastic wrap.
Refrigerate until firm enough to slice, at least one hour or overnight.
Preheat oven to 350 degrees F and put the rack in the middle of the oven.
Line a baking sheet with parchment paper.
Remove the dough from the plastic and slice into ¼ inch thick circles. Place 1 inch apart on baking sheet.
Bake 12-15 minutes, rotating baking sheet half way through baking time.
Cookies will puff a little then deflate. They will be finished about 1 minute after they deflate. They will be dry but soft.
Slide cookies and parchment on a rack and let cool completely.
If cookies aren't as crisp as you would like after they have cooled, you can put them back into the oven for a few minutes.