Preheat oven to 350°F with racks in upper-third and lower-third positions. Line 2 baking sheets with parchment paper. Whisk flour, cocoa, baking powder, baking soda, and salt in a bowl. Set aside.
Whisk brown sugar, granulated sugar, and melted butter in a large bowl. Add eggs and whisk until combined. Add milk and food coloring; whisk until combined. Gently fold in flour mixture using a spatula to form a sticky dough. Cover with plastic wrap, and refrigerate until dough is slightly firm and easy to scoop and roll, about 1 hour.
Place confectioners' sugar in a medium bowl. Scoop dough using a 1 1/2-Tbs. scoop or a spoon, and roll into balls using hands (you should have 24 balls total). Drop dough balls into confectioners' sugar in bowl, and gently toss with your hands to coat well.
Evenly space coated dough balls 2 in. apart on prepared sheets. Bake, rotating baking sheets between top and bottom racks halfway through bake time, until cookies spread and crack, 8 to 10 minutes, Let cookies cool on sheets 10 minutes. Transfer to wire racks, and let cool completely, about 30 minutes.