Combine first 7 ingredients in a large Dutch oven; bring to a boil. Cover, reduce heat, and simmer 1 hour or until chicken is tender. Remove chicken from broth; cool. Strain broth. Bone chicken, and cut into bite-size pieces. Return chicken to broth; set aside.
Combine 2 cups flour and 1 teaspoon salt; cut in shortening with a pastry blender until mixture resembles coarse meal. Stir in hot water with a fork until dry ingredients are moistened. Turn dough out onto a lightly floured surface. Roll dough to 1/16-inch thickness; cut into 1- x 3-inch strips. Bring chicken broth to a boil. Drop dumpling strips into broth. Cover; reduce heat, and simmer 20 minutes or until dumplings are plump and tender. Transfer chicken and dumplings to a serving platter.
Blend 1/3 cup flour with a small amount of water, mixing to form a smooth paste; add to broth, stirring until smooth. Cook, stirring constantly, until thickened and bubbly. Pour over chicken and dumplings.