Put the chicken into a large soup pot. Add container of chicken broth, cover chicken with water, to at least 1/2-inch above chicken. Add 3 stalks sliced celery, 2 peeled and sliced carrots, 1/2 of chopped yellow onion, bay leaves, salt and pepper. Cover, set over high heat and bring to a boil. Reduce heat to low, cover pan and simmer until the chicken is tender, about 1 1/2 to 2 hours.
When chicken is tender, transfer to a cutting board, leaving the broth and bay leaves in the pot. Turn heat off. When chicken is cool enough to handle, remove the meat from the bone and cut into bite size pieces, set aside. Strain broth to remove any leftover bones and skin, discard.
Remove bay leaves from broth. Bring broth back to a boil, add chicken pieces, 2 stalks sliced celery, 3 peeled and sliced carrots and remaining chopped yellow onion. Turn heat to medium and simmer for 45 minutes. Turn broth mixture to a low boil, add cannellini beans and make dumplings.
Make dumplings: In a medium bowl, stir together flour, cornmeal, baking powder, salt and dried basil. Stir in milk until combined. Using a 2 oz. stainless steel, trigger scoop, drop dough into boiling broth mixture. Reduce heat to medium, simmer and cook covered, about 30 to 45 minutes. (Don't lift the lid)