Add the butter to the Thermomix and mix for 30 sec/speed 5 to soften it.
Insert the butterfly whisk, add half the icing sugar and mix for 30 sec/speed 3.5. Scrape down the sides of the bowl.
Add the remaining icing sugar, cocoa powder, vanilla extract and 2 tablespoons of milk. Mix for 20 sec/speed 3, scrape down the bowl, then mix again for 5 sec/speed 3 until smooth.
Remove the butterfly whisk. If there is any unmixed butter at the bottom or cocoa powder on the sides, stir it through with a spatula.
Notes
Storage: Store the buttercream in an airtight container in the fridge for up to 2 weeks, or freeze for up to 3 months. Bring to room temperature and rewhip with the butterfly whisk for a few seconds before using.