Place the whole chicken in a large pot with 2 quarts of water, 2 teaspoons salt, and 1/2 teaspoon black pepper. Bring the liquid to a boil, reduce the heat, cover, and simmer for 1 to 1 1/4 hours, or until the chicken is tender and cooked through.

Remove the chicken from the pot and let it cool until it is comfortable to handle. Pull the meat from the bones, discard the skin and bones, and shred or chop the chicken.

Strain the cooking liquid if needed, then return the broth to the pot. Taste and adjust the seasoning, keeping the broth at a gentle simmer.

Whisk together the flour, baking soda, and salt. Cut in the shortening until the mixture resembles coarse crumbs, then stir in the buttermilk to make a soft dough.

Turn the dough onto a lightly floured surface and knead it briefly. Roll it to about 1/8 inch thick, cut it into strips or squares, and let the pieces rest for a few minutes.

Bring the broth to a steady, gentle simmer and add the dumplings a few at a time, carefully separating them so they do not stick together. Cook uncovered for 8 to 10 minutes, then cover and cook for another 5 to 10 minutes, until tender and no longer floury in the center.

Return the shredded chicken to the pot and heat it through. Taste the broth and add more salt or pepper if needed before serving.