Heat the olive oil in a large Dutch oven or soup pot over medium heat. Add the onion, carrots, and celery; cook 5-6 minutes, stirring occasionally, until softened.
Add the garlic, thyme, and rosemary; stir constantly for about 1 minute until fragrant.
Pour in the chicken broth, scraping up any browned bits. Add the bay leaves, salt, and pepper, then nestle in the chicken breasts. Bring to a gentle boil over high heat.
Reduce to a gentle simmer. Simmer 20-25 minutes until chicken is cooked through (165°F/74°C). Skim foam for clear broth.
Transfer chicken to a board and shred with two forks. Stir egg noodles into broth and cook 6-8 minutes until tender. Return chicken to pot.
Discard bay leaves. Taste and adjust salt and pepper. Stir in half the parsley. Serve with remaining parsley and lemon wedges.