Place chicken and whole onion into the bottom of a large pot.
Pour enough water over the chicken to cover completely. Put peppercorns in a metal tea ball; add to the pot.
Bring water to a boil, reduce heat to medium-low, and cook at a simmer until the chicken until no longer pink and is falling off the bone, 40 to 60 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C).
Remove chicken from the broth with a slotted spoon to a bowl; set aside to cool.
Remove the onion and give it a squeeze to get as much of the flavor as possible. Discard the onion.
Stir carrots, parsnips, and celery into the broth; bring to a boil and cook vegetables until tender, 10 to 15 minutes.
Remove and discard peppercorns.
While the vegetables boil, bring a large pot of lightly salted water to a boil. Cook egg noodles in the boiling water, stirring occasionally until cooked through but firm to the bite, about 5 minutes.
Drain. Divide between 6 soup bowls.
Remove meat from chicken and discard bones.
Cut meat into bite-size chunks and stir into vegetable mixture with parsley. Season with salt. Ladle soup over noodles to serve.
