Place the chicken bones and carcass into a large stockpot and cover with cold water. Bring to a gentle simmer over medium heat, and skim off any foam that rises to the surface. Add the chopped onion, carrots, and celery, then reduce the heat to low and let it simmer gently for about 2 hours, allowing the flavors to deepen and the broth to become clear.
Once the broth has simmered, carefully remove the bones and set aside. Strain the broth through a fine mesh strainer into a clean pot, discarding the solids. Return the strained broth to the stove and bring it back to a gentle simmer.
Add the shredded cooked chicken to the simmering broth. If desired, add a handful of fresh chopped herbs like parsley and dill for extra aroma. Let the soup simmer for another 20-30 minutes, until the vegetables are tender and the flavors meld beautifully.
Taste the broth and season with salt and freshly ground black pepper. Squeeze in lemon juice to brighten the flavors and add a touch of freshness. Stir gently to combine.
Chop additional fresh herbs like parsley and dill, then sprinkle over the soup just before serving for a vibrant, green finish. Ladle the hot soup into bowls and enjoy its comforting, layered richness with tender vegetables and fragrant herbs.
