Preheat the oven to 180 celsius (350 farenheit) and prepare two baking trays by lining them with baking paper.
To make the cookies, combine the butter, sugar and egg yolk in a food processor fitted with a steel blade and process until well combined. Add the flour and cocoa and process until it starts to come together in a ball.
Remove the dough from the food processor and divide into two and flatten into a disc and wrap each disc in cling film and refrigerate for an hour.
Remove one disc of dough from the refrigerator and roll out between two sheets of baking paper until approximately 6mm thick. Using a small circular cookie cutter cut circles from the dough and place onto the prepared baking tray. Bake for 8 to 10 minutes. Roll out the second disc of dough while the first is baking and then bake that when the first tray is done.
Leave the cookies to cool on the tray until firm and then place on a wire wrack to cool.
Once the cookies are cooled make the peppermint cream. Combine the icing sugar, peppermint essence and hot water until it makes a smooth spreadable paste.
Spread the icing mixture onto the cookies and leave to set.
Once the icing has set, place a sheet of baking paper until the wire wrack to catch any chocolate drips. Melt the chocolate over a pot of simmering water and once melted remove from the heat. Dip each cookie in the chocolate and return to the wire wrack to set.
I used Peppermint Essence from <a title="Peppermint Essence" href="http://bakingpleasures.com.au/p9030/peppermint-essence" target="_blank" rel="nofollow" data-mce-href="http://bakingpleasures.com.au/p9030/peppermint-essence">Baking Pleasures</a>, which I found quite strong. You may need to use more or less peppermint essence depending on the brand you use.