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. Keep in mind that you can also over cream here, which will cause your shortbread to spread. Not the end of the world, just something to keep in mind.
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.
Add the chocolate chips and place the mixer on low just to evenly distribute them.
Scrape the dough into a rectangular piece of cling film and wrap. Press the dough down into a rectangle and chill for 30-60 minutes. Pressing the dough into a thinner rectangle helps it chill faster. NB: you can also divide the dough into two logs and refrigerate them this way if you would prefer to cut your shortbread from a log. See the body of the post for notes and comparisons of both methods.
Once chilled, cut half the dough 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.
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.
If you like, roll the edges of the shortbread in 10ml (1/2 tablespoon) milk and then in finishing sugar. This will give your shortbread sugary crusted edges which caramelise beautifully.
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. If you're working in hot weather, refrigerate the dough as necessary and keep the cut shortbreads on their tray in the fridge as you work.
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.