Beat the butter, sugar and vanilla until light and creamy.
In another bowl beat the eggs, add the cinnamon & ginger, baking powder, salt and orange peel, then combine. Sift in the flour, mix gently, then fold in the butter mixture. Stir gently with a spatula until you get a smooth, soft batter.
Form two balls from the mixture, put these in clingfilm, then press down to get a flat disk shape. Chill in the fridge for 2 hours.
Preheat the oven to 180°C.
Remove one of the discs from the refrigerator and roll it out on a lightly floured surface to 50 mm thickness.
Using star shape cookie cutters, stamp out the stars. Kneed together any leftover dough, roll it out again and cut out more stars.
Put the stars on the non-stick or lined baking tray and bake for 12-15 minutes until light brown.
In the meantime roll out and cut out more stars from the other disk of dough. Bake these too.
Let the cookies cool on a wire rack.
Mix the egg white or orange juice with the icing sugar.
Brush the upper side of the cooled cookies with this icing, then scatter desiccated coconut over them. Leave to set.