1. Preheat the oven to 350°F (180°C) and line two baking trays with parchment paper.

For the Dough

1. In a food processor, combine the butter, caster sugar, and egg yolk. Blend until well combined and creamy.
2. Add sifted flour and cocoa powder to the processor. Blend until the mixture starts to come together in a ball of dough.
3. Divide the dough into two portions and flatten each into a disc. Wrap the discs in plastic wrap and refrigerate for 1 hour to chill.

For Rolling and Cutting the Dough

1. Remove one disc of dough from the refrigerator. Roll it out between two sheets of parchment paper to about 1/4 inch (6mm) thickness.
2. Use a small circular cookie cutter to cut out cookies from the dough, placing them on the prepared baking trays.
3. Bake for 8-10 minutes, until firm but not too browned. Allow the cookies to cool on the tray for a few minutes before transferring them to a wire rack to cool completely.
4. Repeat the process with the second disc of dough.

For the Peppermint Cream

1. In a medium bowl, mix together the sifted powdered sugar, peppermint extract, and hot water until it forms a smooth, spreadable paste.
2. Taste the cream and adjust the peppermint extract as needed.
3. Spread the peppermint cream over each cooled cookie and allow it to set.

For Dipping in Chocolate

1. Line a wire rack with parchment paper to catch any drips.
2. Melt the chocolate in a heatproof bowl over a pot of simmering water, stirring until smooth. Once melted, remove from heat.
3. Dip each cookie into the melted chocolate, ensuring they are fully coated. Place the cookies back on the wire rack and let the chocolate set.

Serve

1. Once the chocolate has fully set, your peppermint cream cookies are ready to enjoy!