Place an oven rack in the top third of the oven and preheat to 350ºF (180ºC). Line a baking sheet with parchment paper.
Place the butter in a large microwave-safe bowl. Heat the butter on medium power until it is fully melted. Add the chopped chocolate to the melted butter and stir. If the chocolate does not melt after stirring, reheat the entire bowl for 10-15 seconds.
Add the sugar and cocoa to the bowl. Whisk smooth. Add the eggs and peppermint extract, and again, whisk until smooth.
Sift the flour into the bowl of chocolate and add the baking powder and salt. Switch to a wooden spoon or rubber spatula and fold the wet and dry ingredients together until the flour is just mixed in.
Sift the powdered sugar into a separate shallow bowl. Use a 1½ tablespoon cookie scoop to portion the cookie dough directly into the powdered sugar.
Use a spoon to roll the scoops of dough around in the sugar until they are well coated on the outside. Use your hands to quickly and gently roll the dough portions into balls. Re-dip any bare spots of chocolate into the sugar. Place 12 of the dough balls, evenly spaced apart, on the prepared baking sheet.
Slide the baking sheet into the preheated oven and bake the cookies for 10-12 minutes. Remove the baking tray from the oven and transfer the sheet to a wire cooling rack. Leave the cookies on the sheet to cool before serving or storing.