Stir the fat until frothy. Sift the powdered sugar and mix with the flour, cornstarch, vanilla sugar and aniseed and stir into the fat. Add 1-2 tablespoons of ice-cold water and knead everything well to form a smooth dough. Cover and chill for approx. 30 minutes.
Shape the anise dough into cherry-sized balls, place on two baking sheets lined with baking paper. Slightly flatten the balls with a fork. Then bake them in a preheated oven at 175 degrees for 12-15 minutes. Let cool down. Dust with powdered sugar.