Melt the butter and chocolate together in a heatproof bowl over a pot of simmering water or in the microwave. Stir until smooth.
Whisk the eggs and sugar with an electric whisk until the mixture becomes frothy and light in color.
Combine the melted chocolate mixture with the egg mixture and mix well.
Sift the flour, baking powder, and salt, then gradually add them to the chocolate mixture, stirring until fully incorporated.
Chill the dough in the refrigerator for 1 hour to firm up.
Preheat your oven to 170°C (340°F) and line a baking sheet with parchment paper.
Form small balls from the chilled dough and roll them generously in icing sugar.
Place the balls on the prepared baking sheet, spacing them slightly apart.
Bake for 12 minutes or until the cookies have spread and the tops have cracked.
Let the crinkles cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.