Place chicken and 1 1/2 teaspoons salt in a small Dutch oven, cover with water, and bring to a boil. Cover, reduce heat, and simmer 3 1/2 hours or until chicken is tender. If necessary, add water to maintain at least 3 cups broth. Remove chicken from broth; cool. Bone chicken, and cut into bite-size pieces. Return chicken to broth, and set aside.
Combine flour, baking powder, and remaining salt, stirring well. Cut in shortening with a pastry blender until mixture resembles coarse meal. Add milk, stirring to form a soft dough. Turn out onto a lightly floured surface, and knead gently 30 seconds. Roll dough to 1/8-inch thickness; cut into 2-inch squares. Bring chicken broth to a boil. Drop dumpling squares into broth. Cover; reduce heat, and simmer 10 minutes or until dumplings are plump and tender.
Note: The dough must be rolled very thin to create a good rolled dumpling.