Pour the chicken broth and water into a large stock pot and cook over high heat until boiling.
When the liquid begins to boil, add the chicken and reduce heat to medium. Season with salt and pepper. Simmer until the chicken is cooked through.
While the chicken is cooking, whisk together the flour, baking powder, and salt in a medium bowl.
Add the shortening and use a pastry cutter or fork to cut it into the flour mixture until the mixture resembles coarse sand.
Add the milk and stir until a soft dough forms.
Turn out the dough on a floured surface and roll the dough until it’s around 1/8th inch thick. Cut the dough into equal squares.
When the chicken is finished cooking, remove it from the broth and set it aside.
Drop the dumplings into the broth one at a time to keep them from sticking together. Continue adding the dumplings until all have been added. Cook the dumplings over medium heat for around 20 minutes, until the dumplings begin to float to the top and the broth has thickened.
While the dumplings are cooking, shred the chicken and return it to the pot.
Season the dumplings with additional salt and pepper, as needed, before serving.