Place the whole chicken or chicken parts in a large stockpot. Add 10 cups cold water (enough to cover the chicken by about 1 inch). Add halved onion, carrot piece, celery piece, smashed garlic, bay leaves, thyme sprigs, peppercorns and 2 tsp kosher salt.

Bring to a gentle simmer

Heat over medium-high until the surface just reaches a gentle simmer. Reduce heat to low so the broth barely simmers (small bubbles occasionally). Skim any foam or impurities from the surface with a spoon for the first 10–15 minutes.

Simmer to develop flavor

Continue to simmer gently, partially covered, for 45–60 minutes for parts or 60–90 minutes for a whole chicken, until the meat is cooked through and easily pulls from the bone.

Strain and reserve

Using tongs, remove the chicken to a cutting board and let cool slightly. Strain the broth through a fine-mesh sieve or cheesecloth into a clean pot or large bowl, discarding solids. Taste the broth and adjust salt if needed (add up to 1 tsp more kosher salt if desired).

Prepare Chicken and Vegetables

Shred the chicken

When the chicken is cool enough to handle, remove skin and bones and shred the meat into bite-sized pieces. Reserve about 4 cups of shredded chicken for the soup; freeze or save any extra for another use.

Cook the vegetables

Return the strained broth to the stove and bring to a gentle simmer. Add the diced onion, sliced carrots and sliced celery. Simmer until vegetables are tender, about 8–10 minutes.

Cook Noodles and Finish Soup

Cook noodles separately

While the vegetables simmer, bring a separate pot of salted water to a boil and cook the egg noodles according to package directions until just tender (al dente). Drain and toss with 1 tsp butter or oil to prevent sticking. Cooking noodles separately keeps them from absorbing too much broth and getting soggy.

Combine and finish

Add shredded chicken back to the simmering broth and vegetables to warm through, 2–3 minutes. Stir in cooked noodles, chopped parsley, lemon juice and freshly ground black pepper. Taste and adjust seasoning with additional kosher salt if needed.

Serve

Ladle the soup into bowls, making sure each portion has broth, vegetables, chicken and noodles. Garnish with extra parsley or a squeeze of lemon if desired and serve hot.