Homemade Chicken Noodle Soup

1 (3 1/2-pound) whole chicken
3 quart(s) low-sodium chicken broth
6 carrots, peeled
4 stalk(s) celery, ends trimmed
3 medium onions, peeled
5 black peppercorns
1 clove(s) garlic, crushed
10 sprig(s) parsley
2 sprig(s) thyme
1 bay leaf
2 tablespoon(s) unsalted butter
4 leeks, tops and root ends removed
1 teaspoon(s) salt
1 teaspoon(s) fresh-ground pepper
3 cup(s) (5 ounces) medium egg noodles

DIRECTIONS
Make the stock: Place the chicken and chicken broth in a large stockpot and set it over medium heat. Roughly chop 2 carrots, 2 celery ribs, and 1 onion and add to the broth. Add the peppercorns, garlic, 2 sprigs of parsley, thyme, bay leaf, and enough water to just cover the chicken. Bring the broth to a boil, reduce heat to a simmer, and cook until the chicken is very tender -- about 1 1/4 hours -- skimming the surface periodically. Remove the chicken and place in a large bowl. Strain the broth through a very fine sieve into a large, clean bowl or stockpot. Discard the vegetables.
Make the soup: Skim any fat off the top of the strained broth and discard. Slice the remaining carrots, celery, onions, and leeks into 1/4-inch-thick pieces and set aside. Remove and discard the skin and bones from the chicken, cut meat into 1/2-inch pieces, and set aside. Chop the remaining parsley leaves and set aside. Melt the butter in a large Dutch oven over medium heat. Add the vegetables and cook until the onions are translucent -- about 7 minutes. Add the chicken, the reserved broth, salt, and pepper. Simmer the soup until the vegetables are tender -- about 1 hour. Stir in the egg noodles and parsley and cook until the noodles are tender -- about 10 more minutes. Serve hot.