I usually use a roux etc and, depending on what I use for, I'll add mustard and/or some Worcester sauce. On a James Martin programme however he used milk, cornflour, cheese etc and it does work almost as well and is much easier. I used the milk and cornflour method for brandy sauce at Christmas where the flavour of the brandy dominates.
If it has to be decent then as I was taught at school - make a roux, gradually add milk and stir in a figure of eight, add the cheese at the end - all that brings back horror memories of DS lessons from the school 'fanny'.
Similar to your method but I add a bit of parmesan for extra flavour, just the egg yolk and always Colman's dry mustard. For all my sauces I add the butter, flour and milk in one go and then cook the mixture. Enjoy your meal :)
How did you get away with that, Tilly? I did both.
My needlework teacher was also my form tutor and is the only person who's ever called my "Carrie". She and I stayed in contact after I left school and sometimes met up for a pot of tea on a Saturday.
I make it the same way - but also can add chipotle - great for an adult mac and cheese (bacon/leeks/onions in it and then a mass of cherry toms on top).
People get put off by how the roux reacts to the milk and think they've stuffed it up. Just keep stirring and adding milk. I've never had a cheese sauce go wrong to date.