Add the butter, sugar and vanilla extract to the Thermomix bowl and beat for 20 sec/speed 3. Scrape down the bowl, then repeat for 20 sec/speed 3.
Add the egg and mix for 10 sec/speed 3. Scrape down the Thermomix bowl with a spatula and mix again for 10 sec/speed 3. (the mixture may split, but that's okay).
Add the flour and salt and mix for 10 sec/speed 4. Scrape down the Thermomix bowl with a spatula and then knead for 1 minute (dough setting).
Tip the dough onto a lightly floured board and knead it into a ball shape (be careful not to over-knead). Divide the dough into two portions, cover each with cling film, and then chill in the fridge for 20-30 minutes.
Preheat the oven to 180°C/350°F (160°C fan). Line 2 baking trays with baking paper.
Remove the dough from the fridge. Roll one out to 3-4mm thick. Using a 6cm round cookie cutter, cut rounds from the dough, re-rolling any scraps. Place 3-4cm apart on the trays. Bake in the oven for 8-10 minutes. The edges should be slightly hard but soft in the middle.
Allow to cool on the trays for 10 minutes before transferring them to a wire rack to cool completely. Repeat with the remaining dough portion.
Notes
Storage: The cookies will keep for up to three days stored in an airtight container.To Make Ahead: Wrap the dough in cling film and store it in the refrigerator. When you're ready to use it, let it sit on the bench top to thaw out a little until it's easy to roll.