Heat the olive oil in a large Dutch oven or pot over medium heat. Once hot, add the onion, carrots and celery to the pot. Saute, stirring occasionally, until the vegetables start to soften, about 6 minutes.
Add the garlic to the pot and cook, stirring, for 30 seconds.
Add the chicken broth, dried thyme, salt, pepper and bay leaves to the pot. Stir.
Nestle the chicken breasts into the broth. Slowly bring the soup to a boil over medium heat. Reduce the heat to a low simmer, cover, and cook for 20 minutes, or until the chicken is cooked through and the vegetables are tender. The chicken should register at least 165° F on an instant read thermometer.
Transfer the chicken to a clean plate, cutting board or bowl and let it rest for a few minutes. Then shred the chicken.
Meanwhile, stir the egg noodles into the soup. Increase the heat to medium, cover the pot, and simmer for 6-7 minutes, until noodles are just tender. They will continue to soften as they sit in the soup.
Remove pot from the heat. Remove the bay leaves and discard. Stir the shredded chicken into the soup, along with the chopped parsley and dill. If the noodles have soaked up a lot of the broth, you can add 1-2 cups more broth. Taste and season with additional salt and pepper, as desired. Serve.