Cream the butter with the sugar and vanilla. Sift the flour into the butter and, using a palette knife, mix into a firm dough.
Form a ball, wrap with clingfilm and rest in the fridge for half an hour.
Preheat the oven to 180°C.
Roll out the dough on a lightly floured board to 5mm thick, then stamp out star shapes using a cookie cutter or play-doh cutters.
Place them on a baking tray lined with baking paper and bake for 15-20 minutes until light brown.
Transfer them onto a wire rack to cool. Dust with icing sugar.