Lightly grease two baking trays.
Rub the butter into the flour until the mixture resembles fine breadcrumbs.
Stir in the vanilla sugar, then add the egg and mix well to make a fairly stiff dough.
Knead lightly, then roll out the dough on a floured board to a thickness of 5mm/1/4 in.
Cut into rounds with a 6.5 cm/2 1/2 in fluted cutter and, using a palette knife, carefully transfer the biscuits to the prepared baking trays.
Chill for 30 minutes, or longer if you have time.
Bake in a moderate oven (180C, 350F, gas 4) for 18-20 minutes, or until lightly browned.
Sprinkle the biscuits with vanilla sugar immediately they are removed from the oven.
Leave the biscuits to cool on the trays for a minute before transferring them to a wire rack to cool completely.