Sauté onion in butter in a small Dutch oven over medium heat 5 minutes or until tender. Stir in watercress and salt; cover and cook 5 minutes or until leaves are wilted and tender. Sprinkle flour over watercress; cook 3 minutes, stirring constantly. Stir in chicken broth; simmer 5 minutes.
Place 1 to 2 cups of watercress mixture in container of an electric blender; process until smooth. Transfer pureed mixture to a large saucepan. Repeat procedure with remaining watercress mixture.
Combine egg yolks and whipping cream in a small mixing bowl, mixing well; gradually add 1 cup pureed watercress mixture, stirring constantly. Gradually pour yolk mixture into remaining pureed watercress mixture, stirring well; cook over low heat 2 minutes or until thoroughly heated.
Ladle soup into individual serving bowls. Soup may be served warm or chilled.