In a saucepan, melt the butter then add the flour.
Using a wooden spoon, stir briskly for 1 minute to obtain a roux. Pour slowly the milk over and continue whisking. Bring to the boil and stir continuously with a whick or a spatula for 2 -3 minutes until the mixture boils and become thick and smooth.
Remove from the heat and add some mustard, the cheddar and egg yolk stirring until fully combined. Check the seasoning.