1. Using a stand mixer or hand mixer, cream the butter (creaming technique: beat fat alone until pale and fluffy, about 2 minutes) until light. Add the sugar gradually, beating until the mixture is pale and smooth, about 3 minutes.
2. Add the egg, well beaten, and the salt. Beat until fully incorporated, about 1 minute.
3. Melt the chocolate using a double boiler or in a microwave in 30-second intervals, stirring between each interval, until just liquid. Allow to cool for 2 minutes so it is warm but not hot, then add to the butter-sugar mixture. Beat well until evenly combined and the batter is uniformly dark brown with no streaks.
4. In a separate bowl, whisk together the flour and baking powder. Add the flour mixture and the milk to the batter in alternating additions, beginning and ending with the flour (three flour additions, two milk additions), mixing on low speed after each addition only until just combined. The dough will be soft.
5. Transfer the dough to a lightly floured surface, form into a flat disc, wrap in wax paper or plastic wrap, and refrigerate for at least 1 hour (or up to overnight) until firm enough to roll without sticking.
6. Heat the oven to 425°F (220°C). Line two baking sheets (roughly 13 x 18 inches / 33 x 46 cm, assumed standard half-sheet) with parchment paper.
7. On a lightly floured surface, roll the chilled dough to approximately 1/8 inch (3 mm) thickness. Dip a small round cookie cutter (approximately 2 inches / 5 cm diameter) in flour before each cut to prevent sticking. Cut out cookies and place 1 inch (2.5 cm) apart on the prepared baking sheets.
8. Bake at 425°F (220°C) for 8-11 minutes, until the edges are set and the tops are dry and no longer appear glossy. The cookies will be thin and crisp; they should release cleanly from the parchment and feel firm when lightly pressed. Watch carefully as thin cookies can overbrown quickly in a hot oven.
9. Transfer to a wire rack and allow to cool completely. The cookies will crisp further as they cool.
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