Preheat the oven to 170C/338F. Line two large baking trays with baking paper.
Place the room temperature butter in the bowl of your stand mixer with the paddle attachment. Add the sieved icing sugar and beat on a medium high speed until pale, light and creamy. This can take as few as 3 minutes or as long as 20. Persist until you have the right texture - creamed butter is critical for airy, light shortbread. Scrape down the bowl as often as necessary.
Once the mixture is creamed to your liking, add the flours, salt and vanilla. Process on a slow speed to fully incorporate, then scrape down the sides and turn the mixer to high. If the mixture comes together in large balls without any liquid, don't add any more. If it doesn't, add a teaspoon at a time until it does.
Take a small ball of mixture and roll it in your hands. If the balls crumbles and falls apart, you need to add more liquid. If it's easy to roll, you're good to go.
Scrape the dough into a ball and place it on a clean, dry and floured bench. I use tapioca flour for this purpose. Gently thump the dough down with your rolling pin to flatten it, then begin to roll. Keep picking the dough up as you roll to ensure it doesn't stick. If it crumbles completely as you pick it up, you haven't added enough liquid.
Roll the dough to about 1/2 centimetre (0.19 inches or 1/5th of an inch) and use a circular cutter to cut out your shortbreads. How many you get will depend on the cutter you use. I get around 25 with a 6cm (2.3 inch) circular cutter.
Gently transfer the cut shortbread onto the lined baking tray. If you haven't floured the bench enough you might need to use a thin spatula to pick them up off the counter.
Re-roll any extra pieces until you have used all the dough.
Bake each tray for 20 minutes or until just lightly golden. They are more fragile as they cool so leave them on the tray to cool completely. Store leftovers in an airtight container.