Place the chicken in a large pot and fill with water until it's around 1/2 inch above the chicken. Add 2 tsp salt. Cook on high until the water boils, then reduce to simmer. Skim any scum that floats to the top, then simmer for 45 minutes.
Add vegetables and peppercorns to the pot. Return to a simmer and simmer 1-1 1/2 hours until the chicken meat easily falls off the bone.
Remove the chicken and the carrots from the pot and set aside. Adjust the seasoning of the broth, let it cool, and strain it into a large container, discarding the remaining vegetables. Remove the chicken from the bones and roughly chop.
Meanwhile cook egg noodles according to package instructions.
When the noodles are done, ladle into 6-8 bowls and top with chopped chicken and carrots. Ladle the soup on top and serve. Top with parsley and more pepper if desired.
If you have spare soup and noodles, store the broth and noodles separately or the noodles will continue to absorb liquid in the fridge. The broth will last a fair amount of time of the fridge, and many months in the freezer.