Preheat the oven to 180°C/350°F/gas 4 and line 2 baking sheets with baking paper.
In the bowl of an electric mixer, cream the butter and sugar until light and fluffy.
Beat the egg and stir into the mixture with the peppermint extract, cocoa powder and a tiny pinch of sea salt, mixing until the cocoa is integrated and the batter is smooth and creamy, with the consistency of thick icing.
Add the baking powder and flours, and mix until the batter comes together (don't worry if it’s slightly crumbly).
Turn out the dough onto a floured work surface and knead it just once or twice to bring it together.
Split it in half, flatten each piece into 2½cm-thick discs, then wrap them both in clingfilm. Chill in the fridge for 20 minutes.
Once cool, unwrap the dough onto a well-floured surface and roll it out very thin (about 2½mm thick).
Using a 6cm round cutter, stamp out the cookies. You can make them bigger or smaller if you like – you’ll just need to watch the cooking time.
Place the cookies on the prepared baking trays and use a skewer to pierce little holes at the top for threading the ribbon.
Bake for 7 to 10 minutes, or until firm.
Remove from the oven, transfer to a wire rack and allow to cool completely.
Make the icing by sifting the icing sugar and cocoa into a bowl, then gradually add a few drops of hot water until you have a smooth but thick consistency.
When the cookies have completely cooled, slather them with a little icing and top with the crushed-up candy canes.
Once the icing is set, thread with ribbon and hang from the tree. These will keep for 1 to 2 weeks.