Heat olive oil in a large pot over medium heat. Add the chicken breasts and cook until golden and cooked through. Remove and shred the chicken.
In the same pot, sauté the onion, carrots, and celery until softened.
Pour in the chicken broth and add bay leaves and thyme. Bring to a simmer.
Add the egg noodles and shredded chicken. Cook until the noodles are tender.
In a mixing bowl, whisk the heavy cream with some hot broth, then stir into the soup.
Simmer for a few more minutes, season with salt and pepper, and remove bay leaves.
Serve hot, garnished with fresh parsley.