In a small bowl, sift together the flour, black cocoa powder and salt. Set aside.
In mixing bowl, cream together the butter and the sugar. (Electric or hand mixer is great here.)
Mix in the vanilla and milk until fully combined.
Mix in the dry ingredients, just until fully absorbed.
Press the dough into itself and shape into a log, approximately 1½ inches in diameter. Best to roll the log in parchment paper. Refrigerate 30-60 minutes, then move the log into plastic wrap and roll the log to get it as round as possible. Refrigerate at least another hour.
Preheat oven to 350° F.
Beat the egg. Egg wash the log of cookie dough. Roll in sugar to coat well. Cut slices at least ¼ inch thick and no thicker than ½ inch. Place on a parchment lined baking sheet 2 inches apart. Bake 17-20 minutes. Cool completely.