Using an electric hand mixer, beat the butter and sugar together in a bowl, until pale and fluffy. Add the egg and continue to beat. Sift in the flour, then add the vanilla extract and fold through to form a dough.
Turn out the dough onto a lightly floured surface and knead gently until smooth. Chill in the fridge for 30 minutes.
Preheat the oven to 180°C, fan 160°C, gas 4. Line 2 baking trays with baking parchment.
Remove the dough from the fridge and roll out until it's about 4mm thick. Use a 7cm bunny-shaped biscuit cutter to cut biscuits from the dough.
Arrange on the baking trays and bake for 12-15 minutes, until golden. Remove from the oven and leave the biscuits on the trays to cool slightly before transferring to wire racks to cool completely. Make your bunnies fluffy! Scatter over pink or white sprinkles while the icing is still wet.
To make the icing, combine the icing sugar, milk and a few drops of food colouring in a bowl until smooth. Carefully spread over the biscuits and press a marshmallow tail on each.