Chill the bowl of a food processor. Make sure the fish are very cold.

Process the fish in the food processor until pureed. With the machine on, slowly add the cream in a thin stream, mixing until incorporated. Add the egg whites. Add the salt and pepper and process for 20 seconds, to tighten the mixture.

Transfer to a bowl and chill, covered, in the refrigerator for at least 1 hour.

Bring a large saucepan of water to a boil, then reduce to just a simmer; the water should be at least 2 inches deep. Using a large serving spoon, scoop up some of the quenelle mixture, pressing it against the side of the bowl to smooth the top. (Each quenelle should weigh about 2 ounces, and you should have at least 8.) Place a second serving spoon against the side of the mounded mixture and slide it underneath to lift up the quenelle and shape it further. Scoop up the quenelle with the other spoon again and let it drop into the hot water. Repeat the process to make more quenelles. The water should remain at about 180 degrees. (If the water boils, the quenelles will cook too fast and expand, which they should not do during this first cooking.) Poach for about 12 minutes, turning them over after 5 to 6 minutes.

When they are cooked, remove the quenelles with a slotted spoon and transfer to a bowl of ice-cold water. When they are cold, after about 30 minutes, drain the quenelles, arrange them on a tray, cover, and refrigerate.

Combine the fish bones, onion, leek, celery, bay leaves, thyme, pepper, white wine, and water in a stainless steel saucepan and bring to a boil, then reduce the heat and boil gently for 20 minutes. Strain the stock through a fine strainer into another saucepan. (You should have approximately 1 ½ cups.)

Preheat the oven to 350 degrees.

Process the mushrooms in the food processor until finely chopped. Add to the fish stock, along with the cream, salt, pepper and bring to a boil, then reduce the heat and simmer for 4 to 5 minutes.

Add the dissolved arrowroot to the sauce, stir, and bring to a boil again to thicken; set aside.

Arrange the quenelles in a gratin dish and coat with the warm sauce. Bake for 25 to 30 minutes, until puffy and hot; shake the dish after 10 minutes to be sure the quenelles are not sticking to the bottom.

Serve immediately.