For the stock, place the chicken with the carrots, celery, leeks, peppercorns, bay leaf, thyme, parsley stems and garlic in a large soup pot. Add the water so it just covers chicken. Bring to a boil and reduce to a simmer, partially covered, on low heat. Simmer the mixture for 1 hour until the chicken is cooked.
Transfer the chicken to a plate. Once it is cool enough to handle, remove the skin. Using a fork shred the meat. Discard the bones and carcass.
Pour the stock through a fine mesh strainer into a large saucepan to remove the vegetables and herbs. If you are not using the stock immediately, cool it in an ice bath before refrigerating it up to 1 week or freezing.
For the soup, add the carrots and celery to the chicken stock and simmer until tender, about 10 minutes.
In a medium saucepan, cook the pasta according to package instructions. Rinse under cold water before adding to the stock along with the shredded chicken. Simmer for a few minutes until heated through. Season to taste with salt and pepper. Ladle into bowls and garnish with chopped parsley before serving.