Line 2 baking trays with greaseproof or baking paper.
Place the butter and sugar in a large mixing bowl, then whisk together until pale and fluffy. Sieve in the flour, then add the vanilla extract. Whisk again until the mixture comes together in a dough.
Roll the dough out on a lightly floured surface to around 1cm thick. Cut circles from the dough (I used the fluted side of my cookie cutter), then carefully transfer them to the baking trays.
Place the trays in the fridge to chill for around 20 minutes. Meanwhile, preheat oven to 160°C (Gas mark 2/325°F).
Remove the trays from the fridge and bake for around 15 minutes until golden. Once cooked, leave the shortbread rounds to cool on the baking trays for 15 minutes then transfer to a cooling rack to finish cooling.
Make the buttercream icing. Whisk the butter with an electric whisk until light and fluffy, then sift in the icing sugar, a little at a time, until completely combined. Add the vanilla extract and whisk again. Add the milk in small splashes until the icing is at the correct consistency for spreading.
Once the shortbread cookies are completely cool, spread a generous layer of buttercream icing over the top of each one. Pour the desiccated coconut onto a plate, then dip each cookie, icing side down, into the coconut to coat.
Make the sheep faces - 'glue' 2 candy eyes to each giant chocolate button using the writing icing.
Cut each smaller chocolate button in half for the ears. These will be assembled with the ear pieces behind the giant chocolate button face.
Spread a little leftover buttercream on the back of a giant chocolate button. Press it into the top of a cookie for the head, then push a chocolate 'ear' into the buttercream on each side to finish.
Repeat with the remaining shortbread cookies to turn them into sheep.