Heat oven to 350 degrees. Chop bittersweet chocolate into small bits, and melt over medium heat in a heat-proof bowl or the top of a double boiler set over a pan of simmering water. Set aside to cool. Sift together flour, cocoa, baking powder, and salt.
In the bowl of a heavy-duty electric mixer fitted with the paddle attachment, beat butter and light-brown sugar until light and fluffy. Add eggs and vanilla, and beat until well combined. Add melted chocolate. With mixer on low speed, alternate adding dry ingredients and milk until just combined. Divide the dough into quarters, wrap with plastic wrap, and chill in the refrigerator until firm, about 2 hours.
On a clean countertop, roll each portion of dough into a log approximately 16 inches long and 1 inch in diameter, using confectioners’ sugar to prevent sticking. Wrap logs in plastic wrap, and transfer to a baking sheet. Chill for 30 minutes. Cut each log into 1-inch pieces, and toss in confectioners’ sugar, a few at a time.
Using your hands, roll the pieces into a ball shape. If any of the cocoa-colored dough is visible, roll dough in confectioners’ sugar again to coat completely. Place the cookies 2 inches apart on a Silpat-lined baking sheet. Bake until cookies have flattened and the sugar splits, 12 to15 minutes.
Transfer from oven to a wire rack to let cool completely. Store in an airtight container for up to 1 week.