Second Avenue Deli's Chicken Soup

For those of you not familiar with New York City, the Second Avenue Deli has been an institution for nearly half a century. Here is their delicious version of chicken soup. This is sure to cure the common cold!

1 pound chicken parts, such as necks, backs, and/or wings
1 whole chicken (about 4 pounds)
2 large celery stalks
2 teaspoons salt
1 large onion, with skin, cut in half
1 large carrot, unpeeled, cut in half
1 medium parsnip, unpeeled, cut in half
1/4 tsp. ground black pepper
1 bunch dill, tied with kitchen string

In 8-quart saucepot, heat chicken parts, celery, and 12 cups of water to a boiling high heat.
Rub whole chicken with 1 tsp. salt; add to saucepot. Heat to boiling. Reduce heat to medium-low and simmer, uncovered, 45 minutes, or until chicken is cooked through.
With tongs, carefully transfer whole chicken to plate; set aside. Leave chicken parts in pot.
Add onion, carrot, parsnip, pepper and remaining 1 tsp. salt to pot. Simmer broth over medium-low heat, uncovered, 1 hour and 15 minutes.
When whole chicken is cool to the touch, remove skin and bones; cut meat into bite-size pieces.
Strain broth through fine sieve into large bowl. Discard all solids except carrot. With spoon, skim off fat and discard. Return broth to saucepot. Add dill; let stand 1 minute, then remove. Cut carrot, into 1/4 inch slices; stir carrot and cut-up chicken into soup. Heat through if necessary.