Add the cheese to the Thermomix bowl and grate for 5 sec/speed 9. Tip into a bowl and set aside. There is no need to clean the Thermomix bowl.
Add the butter to the Thermomix bowl and melt for 3 min/60℃/speed 2. Scrape down the sides of the bowl with a spatula.
Add the flour and cook for 1 min/100℃/speed 1. Scrape down the sides of the bowl with a spatula and along the blades. Cook again for 1 min/100℃/speed 1.
Add the milk and cook for 6 min/90℃/speed 4. Add the cheese and blend for 10 sec/speed 5.
Serve immediately, or see notes below on storage.
Notes
Storage: You can store the cheese sauce in an airtight container in the fridge for up to 5 days or freeze it for up to 3 months. If frozen, let it thaw in the refrigerator overnight, then heat it on the stove. It may appear watery but will come together once heated.