Soak rolls in milk. When rolls are soft, squeeze them and force through a sieve.
Sauté the grated onion in half of the butter over very low heat.
After about 6 minutes add chopped mushrooms, and pepper and salt to taste; mix. After 2 minutes add ½cup water. Cook until the water disappears. Let the mixture cool.
Mix together well the egg yolks, sieved rolls, parsley and remaining butter. Add cooled onion-mushroom mixture.
Whip the egg whites until stiff. Gently fold in the bread crumbs, and add to the pudding mixture. Pour into a well-buttered 5-inch metal pudding mold. Do not fill the mold more than three quarters full since the pudding will expand in cooking. Cover the mold tightly.
Make a water bath: Put 2quarts water in a 4-quart pot. Bring the water to a boil and stand the filled pudding mold in it. Cover the water bath. Cook the pudding on top of stove for 1 to 1 ¼ hours.