Sprinkle surface of chicken with salt and pepper. Place chicken in a shallow pan, and pour milk over top. Cover and refrigerate 1 hour. Remove chicken from milk, and dredge in flour. Discard milk.
Heat shortening in a large skillet to 325°; fill with chicken pieces and fry, uncovered, 5 minutes or until brown. Reduce heat; cover and cook an additional 30 minutes or until chicken is tender. Drain chicken well on paper towels. Repeat procedure with remaining chicken pieces.
Place chicken on a warm serving platter, and garnish with parsley sprigs, if desired.