For the chicken stock: Preheat oven to 350 degrees. Rub the chicken with oil, salt, and pepper. Roast for 1½ hours, or when poked with a skewer in the thickest part of the thigh, the juices run clear. Remove from oven and stand to cool. Pour pan juices and fat into a small bowl and reserve. After about 1 hour, pull the meat from the bones and set aside. Place all the bones in a 5-quart stock pot and cover with water. Add onion, celery and bay leaves, bring to a rolling boil and lower to a simmer. Simmer for 1½ to 2 hours. Strain and reserve liquid and lightly season with salt and pepper.
For the chicken and dumpling sauce: In a 2-quart saucepot add chicken fat, onions, mushrooms and garlic and stir to sauté for 2 to 3 minutes or until onions become soft and opaque. Add the flour and stir another 3 to 5 minutes. Add the remaining pan juices, stock and cream, bring to a low boil and reduce to a simmer. Lightly season with salt and pepper. Simmer for 20 minutes. Add green onions
For the dumplings: Sift the flour, baking powder and sugar into a large bowl. In a small bowl combine the beaten egg and milk to a smooth mixture. Make a well in the center of the dry ingredients, add the milk and egg mixture and stir in. Fold in the parsley.
To assemble: Coarsely chop the pulled chicken meat and add to the chicken and dumpling sauce. Bring sauce to a low simmer and drop the dumpling mixture by large spoonfuls into the simmering sauce. Cover and simmer for 10 minutes. Stir and check seasoning. Serve in a soup tureen, deep platter or individual soup bowls.