Preheat oven to 160oC. Line a baking tray with baking paper.
Combine sieved flour, rice flour, sugar and salt in a bowl. Add the vanilla extract. Rub in butter and knead gently until smooth dough forms.
Flatten dough into a disk, wrap in cling film and refrigerate for 1 hour.
Remove from fridge and roll to 1 cm thickness. Cut rounds or other shapes using a lightly floured cutter.
Carefully insert stick into shortbread shape. If dough tears, use extra dough to mend tear with your fingers. Pinch the bottom of the dough where it meets the stick to ensure that it is secure.
Gently place cookies and stick on the tray and place in fridge for another 15 minutes.
Bake in the oven for 13 to 15 minutes until slightly golden on edges but still pale in the centre. Allow to cool. Decorate.