In a large stock pot or Dutch oven, heat two tablespoons of olive oil or butter over low-medium heat. Add the carrots, celery, and onion. Cook the vegetables for 7 to 8 minutes until they begin to soften and the onions become translucent. Add the garlic and cook for an additional 30 seconds.

Next, add the bay leaves, thyme, salt, pepper, broth, and chicken breast. Bring the soup to a simmer and cook over medium heat for 1 to 1 ½ hours or until the chicken is cooked through and easily shreds with a fork.

Remove the chicken breast to a waiting plate and use two forks to shred. Discard the thyme sprigs and bay leaves, then return the shredded chicken to the pot along with the fresh parsley. Stir to combine.

Serve hot. Store leftovers in the refrigerator for up to 3 days.