Using an electric mixer, beat butter, sugar and vanilla until well combined. Use a wooden spoon to stir in flour and enough milk to form a soft dough.
Turn dough out onto a lightly floured surface. Knead until smooth. Divide dough in half. Press each half into a 10cm (diameter) round. Wrap separately in greaseproof paper and refrigerate for 40 minutes, or until firm.
Preheat oven to 160°C. Line 2 baking trays with non-stick baking paper. Roll dough out between 2 sheets of baking paper to 5mm thick.
Cut out shapes and place onto lined tray. Refrigerate until firm. Press leftover dough together. Repeat until all dough is used.
Bake biscuits for 12 to 15 minutes, or until golden and cooked through. Transfer to a wire rack to cool.
Make icing: Combine icing sugar and enough water to form a thick icing. Add a few drops of food colouring. Stir until well combined. Spoon icing into a small snap-lock bag. Snip off 1 corner. Pipe icing over biscuits to decorate. Allow to set.
