For the broth: Place all ingredients for broth into a 6-quart pot. Cover and bring to a boil, reduce heat to med-low and simmer for 1.5 hours. Strain broth into a large bowl. Place chicken breasts onto a plate to cool. Pour the broth back into the pot. Once chicken is cooled, remove the skin, pull the meat from the bones and chop the chicken into bite size pieces.
Place all of the veggies for the soup (onion, carrot, celery, and shiitake mushrooms) into the pot with the broth. Cover and simmer for about 15-20 mins. Add the chicken. Season with salt and pepper to taste. Simmer a minute or two more until the veggies are soft. Enjoy!