Combine first 9 ingredients in a Dutch oven. Bring to a boil; partially cover. Reduce heat; simmer 45 minutes or until chicken is done. Transfer chicken and vegetables to a large bowl, using tongs; cool slightly.
Bring broth to a boil. Separate frozen dumpling strips; break each strip in half. Add dumplings to broth, 1 at a time, stirring often to prevent sticking. Cover, reduce heat, and simmer 25 minutes.
Meanwhile, remove chicken from bones; cut meat into bite-sized pieces.
Add chicken, butter, and pepper to dumpling mixture; stir well to combine. Simmer 10 minutes, covered, or until dumplings are tender.