Place the chicken bones on a baking sheet and broil until deeply charred and smoky, about 10 minutes. This step develops a rich, smoky flavor in the broth.
In a large heavy-bottomed pot, heat a tablespoon of olive oil over medium heat. Add chopped onion and minced garlic, sautéing until fragrant and translucent, about 5 minutes.
Add the roasted chicken bones to the pot, then cover with about 8 cups of water. Bring to a gentle simmer and skim off any foam that rises to keep the broth clear.
Reduce heat to low and simmer gently for at least 2 hours, allowing the flavors to deepen and the collagen to break down, filling your kitchen with a savory aroma.
While the broth simmers, char the carrots and celery in a dry skillet or under a broiler until they develop dark, smoky edges and are tender when pierced, about 10 minutes.
Strain the broth through a fine-mesh strainer into another pot, discarding solids, and return the clear broth to a clean pot.
Add the charred carrots and celery to the strained broth, along with shredded cooked chicken if using. Bring to a gentle simmer and cook for another 20 minutes to meld the flavors.
Stir in freshly squeezed lemon juice and zest, then season with salt and pepper to taste. Taste and adjust the seasoning as needed for brightness and balance.
Finish with a generous sprinkle of chopped fresh herbs and a drizzle of olive oil just before serving. The broth should be clear, fragrant, and slightly smoky with tender vegetables and juicy chicken pieces.
Ladle the warm soup into bowls, garnish with extra herbs if desired, and enjoy a comforting, flavor-packed bowl of smoky chicken soup.
