Allow the lamb shoulder to thaw under refrigeration for 3 days. Place on a foil-lined sheet pan and rub the outside with olive oil.
Using a propane torch, sear the top, bottom and sides. Rub the Turkish Smoking Rub on all sides of the lamb shoulder.
With the fat side up, place on a 225°F indirect grill or smoker, using only lump charcoal. Cook for two hours.
After two hours, wrap the lamb shoulder in plastic wrap then tightly with aluminum foil. Raise the grill or smoker temperature to 300°F and place the lamb shoulder back on the grill or smoker for an additional two hours. The internal temperature should reach about 200°F.
Remove the lamb shoulder from the grill or smoker and keep it in foil for about 30 minutes, until somewhat cooled.
Remove the foil and plastic. Shred the meat. Either place in a bain-marie to keep warm or in a refrigerated storage container for future service.
SERVE THE LAMB SHOULDER:
Place the desired portion of warmed lamb shoulder in a stainless mixing bowl and lightly dust with more Turkish Smoking Rub. Mix to combine.
Serve the meat with warmed pita bread, tzatziki, hummus, or Greek yogurt.