Cook bones and vegetables in 1 1/2 quarts water for about 2 hours. Keep skimming the broth to remove scum. Strain. Add enough water to bring the amount to 1 1/2 quarts again. Add barley to the broth and cook until it is soft.
Make a roux with butter and flour. Cook the roux over low heat, stirring constantly, but do not let it become dark. This should be a light roux. Stir 1/3 cup cold water and 1/3 cup cold milk into the roux and whip until smooth. Pour into soup and simmer it for 10 minutes.
Puree the soup in a blender or through a sieve. Adjust the salt to taste. Mix cream with egg yolk and put it in a soup tureen. Just before serving, pour hot creamed soup over the yolk and cream mixture.