Preheat oven to 170C. Line 2 large baking trays with baking paper. Use an electric mixer to beat the butter and caster sugar in a bowl until pale and creamy. Divide mixture in half. Add a few drops of red food colouring to 1 portion and mix well.
Divide the flour between the portions and use a non-serrated knife in a cutting motion to mix until a soft dough forms. Bring each dough together and flatten into a disc. Wrap in plastic wrap and place in the fridge for 15 mins or until firm enough to roll.
Roll out 1 dough portion between 2 sheets of baking paper until 5mm thick. Use a 6cm star cutter to cut out stars, re-rolling when necessary. Repeat with remaining dough portion. Place on the lined trays. Bake for 15 mins or until golden underneath. Cool on trays for 5 mins, then transfer to a wire rack to cool completely.
Use an electric mixer to beat extra butter and icing sugar until pale and creamy. Divide the icing in half. Add a few drops of red food colouring to 1 portion and combine. Place in separate small piping bags fitted with a small star nozzle. Pipe white icing onto half the red biscuits. Top with the remaining red biscuits. Repeat with red icing and plain biscuits. Dust lightly with extra icing sugar.