Butter the mold and sprinkle with cheese. Measure out ingredients. Preheat oven to 400 degrees.
Grind half the fish; you will have ⅔ to ¾ cup of purée. Set it aside. Following directions for fish filets in white wine, season the rest of the filets, arrange them in a buttered baking dish with the shallots, wine, and enough water barely to cover them. Bring to the simmer, cover with buttered paper, and bake in bottom third of oven for 8 to 10 minutes or until a fork just pierces them easily. Strain out all the cooking liquor, boil it down in an enameled saucepan until it has reduced to ¼ cup, and set it aside until later for your sauce mousseline sabayon.
Cook the flour and butter together slowly in the saucepan for 2 minutes without coloring. Off heat, beat in the boiling milk, salt, pepper, and ground fish. Boil, stirring, for 2 minutes.
Remove from heat and immediately beat in the egg yolks one by one. Taste for seasoning.
Beat the egg whites and salt until stiff. Stir one fourth of them into the soufflé mixture. Stir in the cheese. Delicately fold in the rest of the egg whites.
Filling the mold
Turn a third of the soufflé mixture into the prepared mold. Cut the poached fish filets into 2-inch strips about ½ inch wide, and arrange half of them over the soufflé. Cover them with half the remaining soufflé mixture, and arrange the rest of the filets over it. Cover them with the last of the soufflé mixture.
Beat the egg yolks, cream, and fish liquor over low heat until they gradually thicken into a light cream that coats the wires of the whip (165 degrees). Do not overheat or the egg yolks will scramble.
Off heat, beat in the butter a piece at a time, beating until each is almost absorbed before adding another. The sauce will thicken like a hollandaise.
Taste carefully for seasoning, and add drops of lemon juice if you feel they are needed. Keep sauce over tepid—not hot—water, and when the soufflé is done, pour the sauce into a warm sauceboat to accompany the soufflé.