Place the rinsed chicken bones and carcass in a large stockpot, then cover with cold water by a few inches. Bring to a gentle simmer over medium heat, filling your kitchen with a meaty aroma.
Skim off any foam that rises to the surface in the first 15 minutes, using a ladle. This keeps your broth clear and clean-looking.
Add the roughly chopped onion, carrots, and celery to the pot. Stir briefly and let everything simmer gently, uncovered, for at least 2 hours, filling your space with a fragrant aroma.
Check occasionally, adding more water if needed, to keep the ingredients submerged. The broth will become rich, slightly gelatinous, and golden in color.
Once done, turn off the heat and strain the broth through a fine sieve into another pot or large bowl. Discard the solids, leaving behind a clear, aromatic liquid.
Season the broth with salt and freshly ground pepper, tasting and adjusting until perfectly balanced.
Shred the cooked chicken meat into bite-sized pieces, then add it to the hot broth along with the chopped herbs. Squeeze in a bit of lemon juice for brightness and stir gently.
Finish by drizzling a good-quality olive oil over the soup, giving it a final stir. The broth should shimmer and smell inviting.
Ladle the steaming soup into bowls, garnish with extra herbs if desired, and serve hot for ultimate comfort.