In a large pot combine chicken, carrots, onion, celery, peppercorns, and bay leaf. Cover with water and bring to a boil. Reduce heat and simmer for 1 to 1 1/2 hours. When meat is falling off the bone, remove the chicken from the pot and set aside to cool. Strain and reserve to remove vegetables and reserve stock. When chicken is cool, remove all meat from the bones and shred.
In a large heavy pot, heat oil over medium high heat. Stir in onion and cook for 1 minute. Stir in carrots, celery and potatoes and toss to coat. Cook vegetables for 3 minutes. Stir in flour and cook for 2 minutes. Add reserved stock and stir until it thickens. Add an additional cup of water if more liquid is needed. Simmer for 30 minutes or until vegetables are tender. Stir in chicken and parsley and season with salt and pepper.
For the dumplings: In a large bowl, stir together the flour, baking powder and salt. Using a pastry blender, two knives or your fingertips cut the butter into the flour. Stir in the milk and parsley. Drop by the spoonful into the simmering stew. Simmer for 8 minutes or until firm.