Preheat your oven to 400°F (200°C) and spread the chicken bones on a baking sheet. Roast for about 30 minutes until they develop a deep, smoky color and smell rich and roasted.
Meanwhile, chop onions and garlic, and prepare carrots and celery by cutting them into thick slices and chunks respectively.
In a heavy-bottomed pot, heat a tablespoon of olive oil over medium heat. Add the onions and garlic, sautéing until fragrant and translucent, about 5 minutes.
Add the roasted chicken bones to the pot, cover with water, and bring to a gentle simmer. Skim off any foam that rises to keep the broth clear.
Let the broth simmer gently for at least 2 hours, stirring occasionally, until flavors deepen and collagen releases, creating a rich, slightly gelatinous broth.
While the broth simmers, char the carrots and celery in a dry skillet or under the broiler until they develop smoky edges and are tender, about 8-10 minutes.
Strain the broth through a fine-mesh strainer into another pot, discarding solids. Return the clear broth to the stove and bring to a gentle simmer.
Add the charred vegetables and shredded cooked chicken to the broth. Warm through for about 10 minutes, allowing flavors to meld.
Squeeze in the juice of a lemon and add lemon zest to brighten the broth. Season with salt and pepper to taste, adjusting as needed.
Finish the soup with a drizzle of olive oil and sprinkle with chopped fresh herbs for a burst of herbal freshness.
Serve the hot, smoky chicken soup in bowls, enjoying the rich, aromatic broth with tender vegetables and succulent chicken pieces.