Place chicken in Dutch oven; add water and 1 teaspoon salt. Bring to a boil; cover, reduce heat and simmer 1 hour or until tender. Remove chicken and let cool slightly. Bone chicken; cutting meat into bite-size pieces; set aside. Bring broth to a boil; add pepper.
Combine flour, soda, and 1/2 teaspoon salt; cut in shortening until mixture resembles coarse meal. Add buttermilk stirring with fork until dry ingredients are moistened. Turn dough out onto a well floured surface, and knead lightly 4 or 5 times.
For drop dumplings, pat dough to 1/4 inch thick. Pinch off dough to 1 1/2 inch pieces and drop into boiling broth. Reduce heat to medium low, and cook 8 to 10 minutes or to desired consistency stirring occasionally. Stir in chicken.
For rolled dumplings roll dough to 1/4 inch thickness. Cut dough into 4 x 1/2 inch pieces. Drop dough one piece at a time into boiling broth, gently stirring after each addition.