(4-lb.) fresh whole chicken, cut up
medium onion, peeled and chopped
stalk celery, trimmed and chopped
cup butter or margarine (or a combination), melted
cups boiling water
Place cut-up chicken in a large pan filled with enough water to completely cover chicken. Add onion and celery, cover pan and simmer until chicken is tender - about 35 to 40 minutes. Remove chicken and cool, reserving liquid. Debone chicken and cut meat into pieces; set aside. For the dumplings, combine butter and boiling water in medium heavy saucepan over medium heat. Stir in the first addition of flour and salt; cook until mixture just pulls away from the sides of the pan, about 3 minutes; cool slightly then beat in eggs, one at a time. Pat dough out on a floured surface to about ½-inch thickness; cut into small, irregular strips, 1½ to 3 inches long. (They will resemble short, fat noodles.) Make a paste with remaining flour and water; bring reserved chicken stock to a boil, reduce heat, and whisk in the flour paste to dissolve. Stir constantly until thick, then add chicken and dough, adding extra water (or canned chicken broth, if desired) if necessary to achieve more soup-like consistency; cook until dough is done, about 5 minutes.