Combine brown sugar, salt, pepper, paprika, garlic, Italian seasoning, onion powder, chili powder, cayenne pepper, cumin, and sage in a small container. Measure 1 tablespoon of the dry rub mixture into a large container that will fit the pork butt. Refrigerate remaining dry rub.
Mix apple cider, 1/4 cup apple juice concentrate, 2 tablespoons honey, Worcestershire sauce, and liquid smoke into the large container to make marinade.
Score top of pork butt in a checkerboard pattern. Inject some of the marinade into the bottom, sides, and top of the pork butt. Place pork in the container with the remaining marinade. Marinate in the refrigerator, 8 hours to overnight.
Combine whiskey barrel wood chips, apple wood chips, 1/2 cup apple juice concentrate, and water in a large resealable bag. Seal and let soak, about 20 minutes.
Preheat an electric smoker to 225 degrees F (110 degrees C). Fill smoker box with wood chips according to manufacturer's instructions.
Remove pork from marinade; rub mustard and 1 tablespoon honey evenly on top. Coat pork butt heavily with dry rub. Place fat-side up on a rack.
Place the rack in the smoker; cook until an instant-read thermometer inserted into the center reads 160 degrees F (71 degrees C) for medium or 170 degrees F (77 degrees C), 4 to 6 hours. Add additional soaked wood chips halfway through cooking time.
Place pork butt fat-side up on a large platter. Cover with aluminum foil and let rest for 20 minutes, turning over halfway through resting time.
Use fresh herbs instead of dried in the rub, if desired.
Use orange concentrate or a combination of apple and orange in the marinade, if desired. Concentrated juice may be substituted with fresh. You'll need to cut down or eliminate the amount of water if fresh juice is used.
You may use all apple or all Jack Daniel's® wood chips. Other wood types will change the flavor.
Smoking time may be adjusted as desired. Meat will continue to cook while resting, so I recommend removing it just before desired doneness is reached to avoid overcooking.
Nutrition data for this recipe includes the full amount of marinade and dry rub. The actual amount of marinade and dry rub consumed will vary.