Place chicken in a large deep pan such as a Dutch oven or a saucepan. Add water and salt; it should cover the chicken pieces by about an inch. Place over medium-high heat and bring to a gentle boil.

Reduce heat to a lively simmer, and cook for 35 to 45 minutes, or until chicken is tender and cooked through. Remove from heat.

When chicken is cool enough to handle, remove skin and bones and pull meat into big pieces. Cover and refrigerate.

Meanwhile, combine the flour, salt and pepper in a medium bowl, using a fork. Make a well in the center of the flour and pour in about 1/4 cup of hot chicken stock. Stir well with a fork, until the flour comes together into a rough, shaggy dough.

Turn out onto a floured board or bench top, and knead for about 3 minutes, until you have a fairly smooth, resilient dough.

Scatter flour over the bench top. Divide the dough into 3 portions. Using a rolling pin, roll out each portion into a thin, flat sheet.

Cut into strips about 1 1/2 to 2 inches wide. Cut strips crosswise into pieces about 2 inches long.

Measure the chicken broth, you should have about 7 cups. If you don’t have that much, add water or chicken broth to make 7 cups. Bring the chicken broth to a lively boil. Reduce the heat to maintain a very gentle simmer. Add the dumplings, a few at a time, stirring to keep them from sticking together.

When all the dumplings are in the pot, stir well. and let cook 20 minutes, until the dumplings have thickened a little and become silky smooth outside and cooked within.

Return the chicken pieces to the pot. Cook and stir gently to combine everything well and heat the chicken pieces through. Season to taste with salt and pepper.

Serve in shallow bowls, with dumplings, chicken, and broth in each bowl.