Cream together the butter and the sugar, by hand, in a large bowl until just incorporated.
Slowly add the eggs, again beating the mixture by hand.
Add the peppermint and stir until the peppermint is throughout the mix.
Add the flour and cocoa powder to the bowl and, using a spatula, begin to mix the wet and dry ingredients.
As the ingredients come together, use your hands to work the ingredients into a dough.
Place the dough in the fridge for at least an hour (or roll out until it is roughly 0.5cm thick and refrigerate for at least half an hour).
Roll out the dough on a very lightly floured surface and cut out using a star cookie cutter.
Place the cookies back into the fridge for at least another 10 minutes before baking in the centre of your oven for 8-12 minutes.
Let the cookies cool completely before moving on to decoration.
To decorate, melt the milk chocolate and poor into a small disposable icing bag.
Cut a very small hole into the end of the piping bag and drizzle across the top of the cookies.
Repeat the process with the white chocolate.
Leave the chocolate to cool and set completely before eating.