Clean chicken; cut into pieces and place in large pot with water (enough to cover) and boil until tender (skim top).
Remove chicken and, when cooled, remove meat from bones.
While chicken is cooling, add enough water to broth to make 2 quarts and finely chopped celery, green onions, chopped parsley, chicken bouillon cubes and salt and pepper to taste. Let simmer while you debone chicken and make dumplings.
Dumplings: Combine flour and oil or Crisco.
Use milk to make manageable dough and roll thin.
Cut in strips about 1 1/2-inches wide and then 4 to 5-inch strips or break pieces and drop in briskly boiling broth, one at a time, and move around so they will not stick together.
After you get them all to boil for a few minutes, cut down heat; simmer covered 10 minutes.
If you don't have enough broth, add boiling water for more gravy in dumplings.