Heat the olive oil in a large Dutch oven over medium heat. Add the onion, carrots, and celery; cook, stirring occasionally, until beginning to soften, 5 to 6 minutes. Stir in the garlic for 30 seconds.
Add the broth, chicken, thyme, bay leaf, salt, and pepper. Bring to a gentle simmer. Cook until the thickest part of the chicken reaches 165°F (74°C), about 18 to 22 minutes depending on thickness.
Transfer the chicken to a plate. Add the egg noodles to the simmering broth and cook according to the package directions, usually 6 to 8 minutes, until tender.
Shred or slice the chicken, discard the bay leaf, and return the chicken to the pot. Stir in the parsley and optional lemon juice. Taste and adjust the seasoning, then serve.
Ladle into bowls and serve hot. Add extra parsley or a squeeze of lemon at the table if desired.