Place the whole chicken in a large heavy-bottomed pot and cover with cold water. Turn the heat to medium and bring to a gentle simmer, skimming off any foam that rises to keep the broth clear.
While the chicken simmers for about 10 minutes, dice the onion, chop the carrots and celery, and mince the garlic.
In a separate pan, heat olive oil over medium heat. Add the diced onion, carrots, and celery, sautéing until fragrant and slightly softened, about 5 minutes.
Add the sautéed vegetables to the simmering broth, along with the minced garlic and fresh herbs. Reduce the heat to maintain a gentle simmer and cook for 1.5 to 2 hours until the chicken is tender and falling off the bone.
Once cooked, remove the chicken from the broth and let it cool slightly. Shred the meat, discarding any bones or skin.
Strain the broth through a fine sieve into a clean pot, pressing gently on the solids to extract maximum flavor and clarity.
Return the shredded chicken to the strained broth, add chopped greens if desired, and season with salt, pepper, and a squeeze of lemon juice for brightness. Let simmer for another 5 minutes until greens are wilted and flavors meld.
Taste the soup and adjust seasoning as needed. The broth should be clear and golden, with tender vegetables and flavorful shredded chicken.
Serve the hot chicken soup in bowls, with a wedge of lemon on the side for an extra bright note. Enjoy the comforting, nourishing warmth!