Cook the onions slowly in the butter in a covered saucepan for 5 to 10 minutes, until tender and translucent but not browned.
Stir in the water cress and salt, cover, and cook slowly for about 5 minutes or until the leaves are tender and wilted.
Sprinkle in the flour and stir over moderate heat for 3 minutes.
Off heat, beat in the boiling stock. Simmer for 5 minutes, then purée through a food mill. Return to saucepan and correct seasoning.
(*) If not to be served immediately, set aside uncovered. Reheat to simmer before proceeding.
Blend the yolks and cream in the mixing bowl. Beat a cupful of hot soup into them by driblets. Gradually beat in the rest of the soup in a thin stream. Return soup to saucepan and stir over moderate heat for a minute or two to poach the egg yolks, but do not bring the soup to the simmer. Off heat, stir in the enrichment butter a tablespoon at a time.
Pour the soup into a tureen or soup cups and decorate with optional water-cress leaves.
TO SERVE COLD: Omit final butter enrichment and chill. If too thick, stir in more cream before serving.