In a large pot, combine chicken breasts, onions, minced garlic, bay leaf, and water or chicken broth. Bring to a boil.
Boil until chicken can be easily pulled away from the bones, about 30-45 minutes.
Remove chicken from pot and set aside to cool until safe to handle.
Add chopped celery and carrots to the broth and bring back to a simmer.
While vegetables cook, shred or cut the cooled chicken into bite-sized pieces.
Return chicken pieces to the pot with the simmering vegetables.
Continue simmering until vegetables are almost tender, about 10-15 minutes.
Add dried egg noodles to the pot and simmer until pasta and vegetables are fully cooked, about 8-12 minutes.
Season with salt and pepper to taste.
Remove bay leaf before serving. Sprinkle shredded cheese on top if desired and stir gently.