Cook onion in 2tablespoons of the butter, covered, for about 10 minutes. Add mushrooms and salt and pepper to taste. Cook, covered, over very low heat till there is no liquid left and only the cooking fat remains. Stir often to prevent burning. Let the mixture cool. Preheat oven to 375°F.
Mix in egg yolks. Whip egg whites till very stiff. Mix them in, and finally mix in bread crumbs.
Spread filling on the stretched strudel dough, and sprinkle with remaining 4tablespoons butter, melted.
Roll the strudel very loosely to leave space for the eggs to swell during cooking (see basic recipe). Place it in a, buttered baking pan, 17 by 11inches.
Bake in the preheated oven for 25 to 30 minutes, till crisp.