Whizz the butter, flour and zest in a food processor until the mixture resembles fine breadcrumbs. Add the icing sugar and egg yolks and mix until smooth. Shape the mixture into a ball. Wrap in cling film and chill for 30 minutes. Preheat the oven to gas 6, 200°C, fan 180°C. Grease two baking sheets. Roll out the dough to 5mm (¼in) thick and cut out as many bunnies as you can using a rabbit-shaped cutter. Bake for 10-12 minutes until golden. Remove from the oven.
Whisk the egg white until frothy. Brush the biscuits with egg, then scatter over the coconut. Return to the oven for 3 minutes. Transfer to a wire rack to cool.
When cool, pipe on the tail in white icing and pipe on the eyes and whiskers in black icing. Leave to set for 30 minutes before serving.