Grind the sole four times, using a fine grinding wheel, or blend in an electric blender on high speed. If using the blender, work on only a little of the fish at a time, blending until the fish is very finely shredded. Then pound it with a wooden spoon.
Place the sole in a mixing bowl and place the bowl over cracked ice. Gradually beat in the egg whites, using a whisk or wooden spoon.
Stir in the cream, a little at a time, making certain it is absorbed after each addition.
Season with the salt, pepper, cayenne and nutmeg. Allow the mixture to stand in the bowl over ice for one hour.
Preheat oven to moderate (350°F.).
Stir the mousse and pour it into a buttered fish mold. Cover with wax paper or buttered brown paper and set the mold in a pan containing one inch of hot water.