Break the dark chocolate into pieces and melt it together with the butter over a bain‑marie (double boiler) until smooth.
In a deep bowl, beat the eggs with the granulated sugar and a pinch of salt until the mixture is pale and lightly foamy.
Add the slightly cooled melted chocolate mixture to the eggs and beat again on low speed for about 1 minute, just until combined.
In a separate bowl, whisk together the flour, cocoa powder, baking powder and vanilla. Sift this dry mixture into the batter in 2 additions, gently folding with a spatula until you get a thick, sticky dough.
Cover and refrigerate the dough for at least 1 hour, preferably 2 hours, until firm enough to shape.
Roll portions of chilled dough into small balls, then coat each ball generously in powdered sugar without shaking off the excess.
Bake at 350°F (180°C) for about 8–12 minutes, until the cookies have spread, developed deep cracks and look just set around the edges while still soft in the center.