Beat the butter and sugar together until smooth. Stir in the egg. Stir in the flour, and form the dough into a ball. Chill for 30 minutes.
Preheat the oven to 190 C / Gas 5. Line a baking tray with baking parchment.
Roll out the dough with a rolling pin between two sheets of baking parchment. Cut the shortbread into fish shapes (or any shape you desire) and place on the prepared baking tray. Form the dough into a ball again, roll and cut until no dough remains. Sprinkle with the vanilla sugar.
Bake in the preheated oven until pale golden brown, about 10 minutes.