To prepare the chicken and broth, place all ingredients in a large Dutch oven or stock pot. Bring almost to a boil, lower heat, cover partially and simmer until chicken is tender, about 2 hours.
Let chicken cool in broth; remove and strain broth, discarding solids. Return broth to pot and bring to a simmer. Cook, uncovered, until it is reduced by one-quarter. Meanwhile, skin and bone chicken and cut into bite-sized pieces. Skim excess fat from broth and cool. Cover and refrigerate chicken and broth until ready to use. You can prepare chicken and broth up to 2 days ahead. Skim solidified fat from top of broth before using.
To make dumplings, sift flour, soda, baking powder and salt into a mixing bowl. Cut in lard or butter with a pastry blender until mixture resembles coarse meal. Make a well in center, pour in buttermilk and quickly stir until dry ingredients are all incorporated.
Lightly flour a smooth work surface and turn dough out onto it. With lightly floured hands, gently push dough away from you to flatten it. Fold it in half, gently pat it out Â½-inch thick, and give it a quarter turn. Repeat until dough is smooth and cohesive, about 20 folds-a little more than you would work biscuit dough. Divide it into 3 equal lumps. Lightly flour and roll one lump out to the thickness of piecrust, about 1/8-inch. Quickly cut into 1-inch wide strips, 2-inches long. Drop dumplings into broth; repeat with remaining dough.
Â Simmer 5 minutes. Add chicken and simmer for 2 to 3 minutes more, until dumplings are cooked through and firm but tender. Taste and adjust seasonings. Ladle into a large bowl or individual soup plates and sprinkle with the remaining parsley.