Shred the cooked fish finely, put it into a small pan with a quarter of an ounce of butter and a dust of salt and pepper, and make it very hot. Separate the yolk and white of one egg, put the white aside, and put the whole egg and the three yolks into a basin, and beat them slightly. Mix the cornflour smoothly with the milk, add it to the eggs, add also the parsley, fish mixture, salt, and pepper.
Melt the remaining half-ounce of butter in an omelet pan, pour in the mixture, and put the pan into a hot oven. Whisk the remaining white of egg stiffly, and when the omelet mixture is thick, heap it over the top, spreading it over roughly. Put the omelet back into the oven till the surface is a pretty pale brown.
Serve it on a hot dish as quickly as possible.