Twelve hours prior to cooking, trim fat cap to 1/4-inch thickness from pork butt. Season heavily with dry rub. Place in plastic bag and refrigerate overnight.
Remove pork from refrigerator 2 hours prior to cooking to come to room temperature.
Prepare smoker to temperature of 210 to 220 degrees F and place 1 handful of hickory chips and 1 handful of apple chips on hot coals.
Place pork butt in smoker and smoke for 14 to 16 hours adding 1 handful of hickory and 1 handful of apple chips every 4 hours. After 5 hours in smoker, begin spraying generously with apple juice every 2 hours.
Pork will be done when the internal temperature reaches 185 to 190 degrees F.
Pull or chop meat as desired and top with your favorite sauce!