Put everything except the noodles in a big soup pot over medium-high heat. Bring it to a boil, then reduce the heat and simmer, uncovered, for about 2 hours, periodically skimming off any foam and debris that rise to the surface. Make the sauce, below, while the soup is, as we say, souping. Refrigerate it so that the flavors can meld together. Remove the chicken and vegetables. Reserve chicken, onions and carrots (if desired), and bring broth to boil again until it is reduced by about 1/3. (This will concentrate the flavors.) Taste and add salt and pepper as desired. Take the chicken meat off the bones, and discard the bones. Cook the noodles according to the package instructions. Ladle soup into a bowl, and add in some shredded chicken, a carrot, some onion and the noodles. Mix everything together. Taste it, and adjust seasoning as desired. (It will keep in the refrigerator for about a week, but bring it to room temperature before serving.) Stir a tablespoon or two into the chicken noodle soup. Get well soon!