Start the broth. Combine the chicken, onion halves, bay leaves, 1/2 teaspoon salt, and 10 cups water in a large pot, bring to a boil, then lower to a gentle simmer.
Cook the bird. Cover and simmer 75 minutes until the thigh reaches 165 degrees F and the meat is tender, skimming foam early.
Pick the meat. Cool the chicken 15 minutes, shred the meat, discard skin and bones, and remove the onion halves and bay leaves.
Add the vegetables. Stir in 2 cups water, celery, carrots, diced onion, garlic, and pepper and simmer 20 minutes until tender.
Cook the noodles. Add the noodles and simmer 8 to 10 minutes until just tender.
Season. Return the chicken to the pot with the butter, herbs, and remaining salt, and simmer 5 minutes.