Serve topped with dumplings.
Combine chicken, onions, celery, bay leaf, and peppercorns in Dutch oven. Add cold water to cover Simmer, covered, 2 hours. Remove chicken and cool. Pull meat from bones and chop. Discard skin and bones. Cool broth, chill, and skim. Return to Dutch oven with chopped chicken. Heat to simmer. Melt butter in small skillet, add flour, and stir to form smooth paste. Slowly add to pot and stir until well blended. Add potatoes, carrots, and beans. Simmer, partially covered, 15 minutes or until vegetables arc tender. Season with salt and pepper.