Sauté the aromatics. In a large soup pot or Dutch oven, heat olive oil over medium heat. Add onion, carrots, and celery. Cook for 5–6 minutes until the vegetables soften slightly and the onion turns translucent.
Add the garlic and herbs. Stir in garlic, thyme, salt, and pepper. Cook for 1 minute until fragrant, this builds the flavor base.
Add the chicken and liquids. Nestle the chicken pieces into the pot, then pour in chicken broth and water. Add the bay leaf. Bring to a gentle boil, then reduce heat to low and simmer uncovered for about 35–40 minutes.
Shred the chicken. Remove chicken pieces from the pot and shred with two forks. Discard bones and return the meat to the soup.
Optional noodles or rice. If using egg noodles, stir them into the simmering broth and cook according to package directions (usually 7–8 minutes). For rice, stir in pre-cooked rice near the end.
Finish and taste. Stir in fresh parsley and adjust seasoning, add salt, pepper, or a squeeze of lemon juice to brighten the flavor. Serve hot with crusty bread or crackers.