Place chicken, onion, and celery in a large pot, and then fill pot with water. Season with poultry seasoning, whole allspice, basil, 1/2 teaspoon salt, 1 teaspoon pepper, and seasoning salt. Bring to a boil. Reduce heat, and simmer for approximately 2 hours, or until chicken is done.
Remove chicken from broth, and strain broth to remove seasonings and any bone. Return broth to pan, stir in cream of chicken soup, and continue simmering. Set chicken aside to cool.
In a medium bowl, stir together eggs, olive oil, 1 tablespoon salt, and 1 teaspoon pepper with 2 cups water. Gradually add flour, and stir until thick.
Using a large spoon and knife, scoop a spoonful of the dough and cut small pieces into the broth. Repeat until all the dough has been used. Stir, cover, and simmer for about 15 minutes.
Meanwhile, skin and debone the chicken. Cut the meat into small pieces, add to the broth, and heat through. Serve.
