Using the food processor, mix the butter, icing sugar and vanilla extract until light and fluffy. Add the sifted flours and cinnamon and pulse until the mixture resembles bread crumbs.
Tip into a large bowl and spoon over the milk and bring the breadcrumb mixture together into a ball as if making shortcrust pastry.
Divide into 2-3 balls to make the mixture easier to manage. Knead the balls of dough on a floured surface until smooth then roll into logs around 6-7cm in diameter. Wrap each log with parchment paper and place in a freezer bag in the fridge for about 1 hour until firm.
Meanwhile pre-heat the oven to 160c and line a couple of baking trays with parchment paper.
When the logs have firmed up, unwrap them and using a sharp knife cut into slices 1cm thick. Place about 3cm apart on the baking trays and bake for around 18-20 minutes until just golden. Cool on wire racks.
Notes
Adapted from Australian Women's Weekly "The Complete Book of Cupcakes, Cheesecakes and Cookies" (I would give you a link but bizarrely, Amazon don't appear to stock it)