Build the broth: Place the whole chicken (or bone-in pieces) in a large pot. Add one quartered onion, 2 carrots cut into large chunks, 2 celery stalks cut into large chunks, garlic, parsley stems (save leaves for later), thyme, bay leaves, peppercorns, and 1 tablespoon salt.
Add cold water to cover by about 1–2 inches.
Simmer gently: Bring to a gentle boil, then immediately reduce to a low simmer. Skim off any foam that rises. Partially cover and cook for 60–90 minutes, until the chicken is very tender and pulls away from the bone.
Remove the chicken: Carefully transfer the chicken to a bowl to cool slightly.
Strain the broth through a fine-mesh sieve into another pot, discarding the cooked aromatics. Taste the broth and season with salt as needed.
Shred the meat: Once cool enough to handle, remove skin and bones. Shred or chop the chicken into bite-size pieces.
Set aside. You’ll have plenty; use what you like and save the rest for leftovers.
Sauté fresh aromatics: In the now-empty soup pot, heat olive oil or butter over medium. Add the diced onion, and sauté 2–3 minutes.
Add sliced carrots and celery. Cook, stirring, until slightly softened, about 5–7 minutes. Season with a pinch of salt and pepper.
Add broth and simmer: Pour the strained broth back into the pot with the sautéed vegetables.
Bring to a gentle simmer and cook until the vegetables are tender, about 10–12 minutes.
Cook the noodles: Add noodles to the simmering broth and cook according to package directions until just al dente. Don’t overcook—they’ll continue to soften in the hot soup.
Add chicken and herbs: Stir in the shredded chicken and chopped parsley leaves. Simmer 2–3 minutes to warm through. Taste and adjust salt and pepper.
If you want a touch of brightness, add a small squeeze of lemon.
Finish and serve: Remove from heat. If you like, sprinkle in a little fresh dill. Ladle into bowls and serve hot.