Set a large 6 to 8 quart pot over medium heat. Add the butter and onions, stir and sauté for 3 to 4 minutes. Then stir in the celery and carrots and sauté another 2 to 3 minutes.

Add the chicken pieces, thyme, bay leaf, and broth to the pot. Season with 1 teaspoon salt and 1/2 teaspoon ground pepper. Stir and bring to a boil, then lower the heat to simmer and cover. Cook for 20 to 25 minutes.

Meanwhile, set out a medium mixing bowl for the dumplings. Add the flour, shortening, salt, and baking powder. Use a pastry blender or large fork to mash the mixture together until it resembles oatmeal. Then mix in the buttermilk until the mixture is mostly smooth.

Dump the dough out onto a floured work surface. Roll the dough out into an even sheet 1/8 to 1/4 inch thick. Use a pizza cutter or knife to cut the dough into 1 by 1.5 inch pieces that look like thick wide noodles.

Once the chicken is cooked through, use tongs to remove the chicken pieces from the broth. Add the dumplings to the broth a handful at a time, stirring gently in between so they don't stick together. Simmer the dumplings for 8 to 10 minutes uncovered, stirring as little as possible.

While the dumplings are cooking, use two forks to shred the chicken pieces. Place the shredded chicken back into the pot along with the parsley. Stir, taste, and add salt as needed. Once the broth has thickened into gravy, turn off the heat and serve.