Place the chicken, celery, carrots, onion, leeks, parsley, peppercorns and bay leaves into a large heavy-bottomed pot or Dutch oven and add enough water so that the chicken and vegetables are covered by about 1-inch of water.
Bring to a simmer over medium heat then reduce heat to low so that the stock is at a bare simmer. Continue to cook, uncovered, until the chicken is very tender and falling off the bone, about 1 hour and 30 minutes. Skim the surface of the broth occasionally.
Use tongs to remove the chicken to a large bowl and let cool. Shred the chicken and add the meat to a bowl, discard the skin and bones. Strain the broth and discard the vegetables. Season to taste with salt.
For serving:
Return the broth to a simmer over medium-low heat and add the diced vegetables. Simmer until the vegetables are tender, about an additional 30 minutes.
Bring a large pot of water to the boil. Pour in the egg noodles and cook, stirring occasionally, until al dente, about 8 minutes. Drain and set the noodles aside.
Add the shredded chicken and the noodles to the broth and continue to simmer for 10 minutes. Ladle the soup into bowls and top with fresh dill.