Grate the cheese into a heatproof bowl with a splash of milk.
Separate 1 large egg, adding the yolk to the bowl (save the white for another recipe).
Sit the bowl over a pan of very gently simmering water, making sure the water doesn't touch the base of the bowl, and leave to slowly melt for 4 to 5 minutes, until silky, almost like a thick custard. Whisk regularly, loosening with more milk, if needed, then season well with black pepper and a few scrapings of nutmeg.
Toss with your dumplings and a splash of their cooking water to loosen, if needed.