Remove pork shoulder from the refrigerator to allow it to begin to come to room temperature.

Load the smoker or grill with the lump charcoal and wood chunks. Light the charcoal and adjust air valves on the smoker until you achieve a steady temperature between 225°F-240°F. (Note: this will likely take about 30 minutes, so plan accordingly!)

Meanwhile, combine all of the spices for the Rub in a small bowl; mix until well combined.

Rub all sides of the pork shoulder with the Rub.

Insert the probe thermometer into the center of the pork. (Note: Make sure probe is not touching bone as that will yield an incorrect temperature.)

Place pork shoulder on the grill and close lid. (Note: Do not open lid again unless you need more charcoal. Lump charcoal is recommended here as it burns longer than charcoal briquettes.)

Occasionally check the temperature of the grill. If the temperature has moved outside of the 225°F-240°F range, then adjust air vents as necessary.

Once the pork shoulder reaches an internal temperature of 190°F-195°F, remove it from the grill and wrap it in aluminum foil. Place pork shoulder in a cooler to rest for 1-2 hours. (This is an important step as it allows the pork to reabsorb the juices.)

Using a carving knife and two forks, shred the pork into smaller pieces.