Whisk the cocoa powder, flour, baking powder, and salt together in a medium bowl.
Melt the chocolate in a heatproof bowl in 20-second microwave increments, stirring between each, then cool for 5 minutes.
Whisk the melted butter, eggs, white sugar, brown sugar, and vanilla into the chocolate.
Stir in the dry ingredients with a wooden spoon until combined; refrigerate the loose dough for 30 minutes.
Heat the oven to 180°C/350°F (160°C fan-forced) and line two baking trays.
Scoop 1 1/2 tablespoons of dough into 20 to 22 balls, roll each in white sugar, then coat thickly in icing sugar.
Bake for 13 minutes until puffed with a light crust and jiggly centers; cool 5 minutes on the trays, then transfer to racks.