Prepare as many small Timbales of Pommes Mirette as there will be Tournedos. When ready, turn them out on to a dish, sprinkle with grated Parmesan and melted butter and gratinate them when the Tournedos are almost ready.
Season the Tournedos and shallow fry in butter.
Arrange neatly on a suitable dish and place one of the prepared Timbales on each.
Serve Sauce Chateaubriand separately.