Heat a large stock pot over medium heat and add a splash of olive oil. Toss in the chopped onion, carrots, and celery. Sauté until fragrant and slightly caramelized, about 8 minutes, until they start to soften and release a sweet aroma.
Place the bone-in chicken into the pot with the vegetables. Pour in the cold water, ensuring the chicken is fully submerged. Bring the mixture to a gentle simmer, around 85°C, and skim off any foam or impurities that rise to the top to keep the broth clear.
Reduce the heat to low, cover the pot loosely, and let it simmer gently for about 1 to 1.5 hours. The broth will turn a rich, golden color, and the chicken will become tender and easily shred with a fork.
Remove the chicken from the pot and set aside to cool slightly. Strain the broth through a strainer if you prefer a clear soup, or leave the vegetables in for a rustic feel. Shred the chicken meat into bite-sized pieces.
Return the shredded chicken to the pot. Add salt, pepper, and a squeeze of lemon juice to brighten the flavors. Warm everything through over low heat for another 10 minutes, allowing the flavors to meld.
Taste the broth and adjust the seasoning as needed. Remove the sprigs of thyme and discard. Ladle the hot soup into bowls, garnish with chopped parsley, and drizzle with a little olive oil if desired. Serve immediately and enjoy the comforting warmth.
