In a medium bowl, beat together the butter and sugar until light and creamy. Beat in the egg yolk, vanilla extract, flour and a pinch of salt. Mix until it forms a dough, then knead until smooth. Wrap in clingfilm and chill for 30 minutes.
Preheat the oven to 180°C/fan 160°C/gas mark 4. Roll out the dough on a floured surface to a thickness of 5mm. Stamp out shapes with cutters and bake on a non-stick baking tray for 10 minutes, until lightly browned. Cool on a wire rack.
Place the icing sugar in a bowl and add cold water, a couple of drops at a time, until the icing has a thick pouring consistency. Spread a little on each cookie and decorate with party sprinkles and sugar stars while the icing is wet.