1Melt shortening to a depth of 1/2 inch in a large heavy skillet to 350 degrees F (175 degrees C). Whisk together the honey and white vinegar; set aside. Whisk together the flour, poultry seasoning, and cayenne pepper in a bowl.
2Season the chicken pieces with salt and black pepper. Roll chicken in the flour mixture to coat evenly; shake off excess. Place the chicken in the preheated skillet, and cook until a light brown crust forms, about 3 minutes per side. Turn the chicken pieces over and brown on the other side.
3Reduce heat to low. Cover the skillet; cook until the meat is no longer pink at the bone and the juices run clear, about 20 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).
4Remove the cover, turn up the heat, and continue to cook, turning as needed, until the chicken is evenly browned and crisp, about 5 minutes. Pour off most of the shortening. Pour the honey mixture over the chicken and cook over medium-low heat, turning chicken pieces to coat, until liquid thickens, about 5 minutes.