Set a large 6 to 8 quart pot over medium heat. Add butter and chopped onions and saute for 3 to 4 minutes until softened. Add celery and carrots and cook another 2 to 3 minutes.

Add chicken pieces, thyme, bay leaf, and chicken stock. Season with 1 teaspoon salt and 1/2 teaspoon pepper. Reserve parsley for later. Bring to a boil, reduce to a simmer, cover, and cook for 20 to 25 minutes.

In a medium bowl, combine flour, shortening, salt, and baking powder. Use a pastry blender or large fork to mix until the texture resembles coarse oatmeal. Stir in buttermilk until the dough is mostly smooth.

Turn dough out onto a lightly floured surface. Roll to 1/8 to 1/4 inch thickness. Cut into 1 x 1 1/2 inch pieces using a pizza cutter or knife to form thick noodle-shaped dumplings.

Remove cooked chicken from the broth using tongs and set aside. Add dumplings to the simmering broth a handful at a time, stirring gently between additions. Simmer uncovered for 8 to 10 minutes. Avoid over-stirring.

While dumplings cook, shred the chicken using two forks. Return shredded chicken and fresh parsley to the pot. Stir gently, taste, and adjust salt as needed. Once the broth thickens into a gravy, turn off the heat and serve immediately.