1 8 lb. pork shoulder (Don't buy an expensive cut of meat. You need a tougher cut as plenty of fat and connective tissue will withstand the long exposure to the heat.)
Barbecued Pork Rub (This is our usual rub for the pork.)
Combine all seasonings.
1/4 cup kosher salt
1/4 cup black pepper
1/4 cup chili powder
1 T. dried oregano
1 T. dried thyme
1 tsp cayenne
Coat the shoulder with the rub, massaging it into the meat.
Grilling Process
Grilling indirectly is for cuts of meat that take a long time to cook. If you don't have a grill with a side compartment, set up your grill so that half has fire and the other half does not. Cooking is done on the area where there is no fire underneath, but there's plenty of heat!
This can be accomplished by placing chunks of wood in a foil pack (use two layers of foil) Bundle the packet leaving a hole at the top so smoke can escape.
Preheat one side of the grill to medium high. Place the smoke packet over the fire, drip pan is under the unlit side.
Place the pork over the drip pan and grill for three hours. Check every hour to make sure there's plenty of smoke. Smoking takes 3 hours. Add wood packets as needed to keep plenty of smoke circulating.
Once smoking is complete, wrap pork in to layers of foil, crimping edges to seal in moisture. Return to grill; cook 2 more hours. After 2 hours, insert thermometer into thickest part of meat. You want to hit 180°. (We cooked the pork at 225°-250° in the smoker for four hours total.)
Keep foil around the meat and let rest off heat for 30 minutes. At this point the meat is ready to be pulled with a fork or fingers. Don't worry about the red ring around the meat. It's not undercooked but rather a natural reaction to the smoke.
After pulling the pork apart and removing and fat that may be remaining, remove the pork you will be eating and mix in some of your favorite BBQ sauce....just a little...do not saturate!
Serve the sandwich on a Kaiser-style bun. (These may be buttered and toasted.) Top the pork with a special coleslaw.