Cut the bread into cubes and finely grate the cheese. Layer alternately in a sufficiently large bowl. Bring milk to a boil and pour over this mixture. Leave to stand for half an hour.
Heat half of the butter in a pan and steam the onion (1) in it until soft. Add the bread-cheese mixture, mix well and let it stand for ten minutes on the off heat.
In a second pan, roast the onion (2) in the remaining butter until crispy and pour over the finished cheese soup form.
By the way: Did you know that clarified butter is obtained by extracting water, milk protein and lactose from butter?