Cook the Chicken: In a large pot, combine chicken, water, bay leaves, and onion. Bring to a boil, then simmer for about 1 hour.
Prepare the Chicken: Remove the chicken, let cool, then shred the meat, discarding the bones.
Simmer the Vegetables: Return the shredded chicken to the pot. Add carrots, celery, and garlic. Season with salt and pepper and simmer until vegetables are tender, about 30 minutes.
Cook the Noodles: In a separate pot, cook noodles until al dente; drain.
Serve: Ladle soup over noodles and garnish with parsley.