Season the pork shoulder with salt, pepper, and any desired spices. Place it in a roasting pan or Dutch oven.
Cover the pan tightly with foil or a lid.
Cook in the oven for 4-6 hours or until the meat is tender and easily pulls apart. Meanwhile, season the chicken livers with salt and pepper.
Heat a pan with the cooking fat and grill the livers for about 2-3 minutes per side or until cooked through but still slightly pink in the center. Serve the chicken livers on the side with the slow-cooked pork shoulder.