Preheat the oven to 170C/325F/Gas 3. Line a baking tray with parchment paper or a silicone mat, and set aside.
In a large mixing bowl, whisk together the butter, vanilla, and sugar until creamy and combined.
Add the cornflour, flour, and salt, and mix to form a smooth, soft dough.
Roll the dough into small 0.7oz balls, and place them onto the prepared baking tray. Press them down with the tines of a fork. Freeze until solid - about 10 - 20 minutes.
Bake for 15 - 20 minutes or until firm and just starting to colour around the edges (they'll still be very pale). Allow to cool for 5 - 10 minutes before transferring them to a wire rack to cool completely.