Cook chicken in water to cover with celery and peppercorns in large saucepan until tender, about 45 minutes. Strain and reserve 2 cups broth. Cool chicken until easy to handle. Skin, bone and cut up enough to make 2 cups. Reserve any meat and broth for another use.
Cook potatoes with 1 teaspoon of the salt and water to cover until tender, about 30 minutes.
Combine broth, mixed vegetables, onions and remaining 1/4 teaspoon salt. Bring to boil, lower heat, simmer 5 minutes. Stir in chicken.
Heat butter in a small pan. Stir in flour with wire whisk until smooth. Cook over low heat for 2 or 3 minutes, being careful not to burn, stirring until smooth; pour all into chicken mixture; spoon all into shallow 6 cup casserole. Mash potatoes with milk, spoon around edge of casserole. Bake at 400 degrees for 20 minutes or until bubbly and potatoes are browned.
