Bring the chicken broth to a boil in a large soup pot. Add the onions, celery and carrots. Turn the heat down to simmer.
In a small bowl mix together the milk, flour and poultry seasoning until smooth. Add to the broth and vegetable mixture and stir well. Let simmer for 10 minutes.
Add the shredded chicken to the pot.
Cut each of the rolls in half. Sprinkle each half with flour (this prevents sticking and thickens the soup). Place each of the roll halves on top of the mixture in the pan. Spoon liquid on the tops of the rolls and cover with lid.
Simmer 20 minutes covered. Uncover and simmer 3-5 more minutes or until the dumplings are cooked through.