Begin by preheating a large heavy-bottomed pot over medium heat. Once hot, add a splash of olive oil to the pot, letting it shimmer. Season the chicken with salt and pepper, then place in the pot. Sear for about 5-7 minutes, turning occasionally until golden brown.

Add chopped carrots, celery, and onion to the pot, stirring well. Sauté the vegetables for about 10 minutes, or until they begin to soften and the onion turns translucent.

Pour in the chicken broth, stirring to combine. Add thyme, increase the heat slightly to bring to a gentle simmer for about 2-3 minutes.

Reduce the heat to low and cover the pot. Allow the soup to simmer for 20-25 minutes, until the chicken is tender.

Remove the chicken from the pot and let it cool slightly before shredding. Return the shredded chicken back to the pot.

Adjust seasoning with salt and pepper, and stir in chopped parsley. Let the soup rest for a few minutes before serving.

Ladle the soup into warm bowls, garnishing with extra parsley if desired. Serve hot with crusty bread or a light salad.