Place the whole chicken, chopped celery, chopped carrots, chopped onion, and 2 teaspoons of the salt in a Dutch oven. Add the 2 quarts water and the bay leaf.
Bring the pot to a boil over high heat. Reduce heat to medium-low, cover, and simmer for 1 hour.
Using tongs or a large spoon, remove the chicken from the pot and set it on a plate. Let it cool 15 minutes.
Remove and discard the skin and bones, and shred the chicken into bite-sized pieces. Set the shredded chicken aside.
Add the black pepper to the pot of broth and bring the broth to a boil.
While the broth is coming to a boil, combine the flour, baking soda, and the remaining 1/2 teaspoon salt in a large bowl.
Use a pastry blender or your fingers to cut the vegetable shortening into the flour mixture until it resembles coarse meal.
Stir in the buttermilk until the dry ingredients are just moistened and a soft dough forms. Turn the dough onto a lightly floured surface.
Knead the dough 4 to 5 times, then roll it out to a 1/2-inch thickness. Pinch off pieces about 1 1/2 inches each and drop them into the boiling broth.
Reduce the heat to medium-low, cover, and simmer the dumplings for 8 to 10 minutes, until cooked through. Stir the shredded chicken into the pot, heat until warmed through, and serve.