Combine chicken, onion, celery, carrot, parsley sprigs, bay leaf, salt, pepper, and water in a large Dutch oven; bring to a boil. Reduce heat; cover and simmer 1 hour.
Remove chicken; set aside. Strain broth through several layers of damp cheesecloth. Reserve vegetables for other uses. Skim fat from broth. Return broth to Dutch oven.
Remove chicken from bones; chop meat, reserving 2 tablespoons chopped chicken for use in Filled Dumplings. Add chopped chicken to broth.
Bring broth to a boil. Reduce heat; add Filled Dumplings to broth. Cover and simmer 10 minutes.
Ladle soup and Filled Dumplings into individual serving bowls; garnish with chopped fresh parsley. Serve warm.