Stir together flour, cocoa, espresso, baking powder, and salt in a medium bowl. Beat butter and brown sugar with a mixer until light and fluffy, about 3 minutes. Beat in egg until well combined; mix in cooled bittersweet chocolate. Reduce speed to low, and gradually add flour mixture; beat in milk until just combined. Cover dough with plastic wrap. Freeze until firm, about 45 minutes.
Preheat oven to 350°F Line 2 baking sheets with parchment. Shape dough into 1/2-inch balls (exactly 1 teaspoon each). Pour confectioners' sugar into a medium bowl; working in batches, roll balls in sugar 2 times, letting them sit in sugar between coatings.
Place on baking sheets, spacing each 2 inches apart. Bake until cookies have spread and coating is cracked, 10 to 12 minutes; cookies will still be soft to the touch. Let cookies cool on a wire rack.