Using an electric mixer, beat the butter, vanilla extract and icing sugar together until smooth and well combined. This will only take a couple of mins if the butter is soft enough.
In a separate bowl, sieve the flour, salt, and cornflour together. Add to the butter mixture. On a low speed, mix until well combined.
Add the white and milk chocolate chips and give everything a good mix. This is probably best done using a wooden spoon.
Turn the dough out onto a baking sheet and bring it all together.
Roll the dough out into a large square about 5 - 6 mm thick. It helps to use a sheet of baking parchment on the top.
Cut into equal portions and place half of the portions onto another baking sheet/baking tray allowing for plenty of space. Place both trays into the fridge for at least 30 mins to allow the dough to firm up. This helps stop the dough from spreading too much during baking.
Baking the Chocolate Chip Shortbread
Preheat the oven to 160 deg (fan assisted oven).
Take the trays of shortbread dough out of the fridge and bake in the centre of the oven for 15 - 18 mins. Or until baked with a very pale golden colour. They may still feel slightly soft to the touch, but they will firm up once cooled.
If you want to separate any that have spread and stuck together, or square off the sides of uneven biscuits, slice the edges with a palette knife while the shortbreads are still warm.
Leave to cool completely before removing them from the baking tray or they could crumble and break.
Decorating with Chocolate
Melt each of the chocolate chips in separate bowls over a pan of simmering water. Take off the heat and let the chocolate cool a little.
When the shortbread biscuits have cooled completely, dip each biscuit into the chocolate at the edges. Spread them out onto a sheet of baking parchment to set. If needed place them in the fridge.
It is important to place the shortbread dough in the fridge to allow the dough to rest before baking. This will help prevent the dough from spreading too much during baking.
Using your hands to bring the dough together, may result in the butter becoming too soft because of the warmth of your hands. Best use a wooden spoon or spatula if you can.
Having cornflour (UK) Cornstarch (USA) in the recipe gives these biscuits a nice light, melt in the mouth texture.
If you cannot get hold of cornflour/cornstarch, use plain flour.
Reduce the recipe by half if you want to make a smaller amount.