Put the cocoa, sugar, flour, baking soda, and salt in the bowl of a food processor and pulse it a couple of times to combine.
Distribute the butter pieces over the top of the flour mixture, and pulse several times until the mixture looks crumbly.
With the processor running, add the peppermint oil, then slowly add the milk and process until a dough forms and rides on top of the blade.
Dump out the dough, knead it a few times to ensure that it's thoroughly mixed, and then shape it into a log about 10 inches long and 1 3/4 inches in diameter.
Wrap with plastic and chill for about an hour.
Preheat oven to 350°F.
Slice and bake. Slice the cookies about 1/8 of an inch thick, place them on a parchment-lined baking sheet about an inch apart, and bake for about 10 minutes. Watch while they’re baking; they’ll puff up a bit, then deflate. Two minutes after they deflate, they're done.