If you're not going to use it straight away, wrap it in plastic wrap, as, like béchamel sauce, it crust quickly.
Remarks
The cheese used is usually a hard one: Comté, Gruyère, Emmental, Cheddar, Parmesan, etc., but you can also use other cheeses to suit your taste, such as Roquefort, Mont d'or or Gorgonzola.
Curiously enough, in his book "Ma cuisine", Auguste Escoffier uses Parmesan and no egg yolks for his version of Mornay.
The name comes from a 19thcentury epicurean named Philippe de Mornay.