For the dough, whisk butter and sugar with the whisks of the mixer until creamy. Stir in the egg yolk. Mix 150 g flour and cocoa. Stir briefly into the butter-sugar mixture. Then knead with your hands quickly to a smooth dough.
Form into a ball, wrap in foil and chill for approx. 30 minutes.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Halve the dough. Roll out one half between two layers of lightly floured baking paper to a thickness of approx. 4 mm (roll out the other half again in the meantime).
Cut out a total of 30-35 circles with wavy edges (each approx. 5 cm Ø), knead the dough again, cool if necessary, roll out and cut out. Place circles on a baking tray lined with baking paper.
Bake in a hot oven for about 12 minutes. Process the remaining half of the dough in the same way. Let the cookies cool down.
For the filling, sieve icing sugar, mix with 4-5 tablespoons of hot water and 2 teaspoons of neutral oil to form a thick cream. Flavour with peppermint oil to taste. Pour into a freezer bag and cut off a small corner.
Spray evenly onto the cookies. Chill for about 30 minutes.
Chop the couverture and melt in a hot water bath. Stir in 1 tsp. oil. Put 1 teaspoon of couverture on each cookie and carefully smooth it down so that the couverture also runs down the edge. Leave to dry on a cake rack.