Combine the chicken and the 2 quarts water in a stockpot. Cook over medium high heat until done, about one hour. Remove the chicken from the pot, reserving the broth. Cool the chicken in cold water. Remove the bones, skin and fat. Cut chicken meat into bite sized pieces. In a mixing bowl, combine the flour and salt. Cut in the shortening until mixure is coarse. Add the 1/4 cup water and mix well with your hands. Bring the chicken broth back to a slow boil. With floured hands, pinch small quarter sized piece of flour and drop them into the simmering chicken broth. Gently stir after adding several pinches. Repeat until all the dumpling mix is used. Stir gently. Add the butter and black pepper. Simmer 8 to 10 minutes. Slowly stir in the chicken meat. Serve in soup bowls.