Pre-heat the oven to 130C (265F) fan-forced and line two baking trays with baking paper.
In the bowl of an electric mixer, beat the butter, lemon zest, ginger and caster sugar together for 5 minutes.
Scrape down the bowl and the beater and beat for another 30 seconds.
Add the flours and mix them through slowly until a dough forms.
Using two level teaspoons of dough at a time, roll it into balls and flatten slightly then place on the oven trays leaving 2cm between each one.
Gently press each one with the back of a fork to make a pretty indent.
Bake for 15 minutes or until firm but not quite golden.
Leave to rest on the trays for 5 minutes then transfer to a wire rack to cool completely.
Dust with icing sugar to serve.