For the broth: Combine all broth ingredients in a large saucepan and cover with cold water by a couple inches. Bring to a boil over high heat, reduce to a bare simmer, and cook, skimming scum and foam from the broth occasionally with a ladle, until the legs are completely tender, 1 to 1 ½ hours. Remove leg and set aside to cool. Strain broth into a new pot and discard the solids.
For the Soup: When the chicken is cool enough to handle, remove it from the bone and shred or chop into bite-sized pieces. Add shredded chicken, carrots, celery, onion, and pasta to the soup. Simmer, stirring occasionally, until the pasta is as cooked as you like it, 10 to 15 minutes. Stir in the herbs, then season to taste with salt and pepper.
