Prepare smoker to 250-275°F.
Trim any hard fat from your whole lamb shoulder.
Combine dry rub ingredients in a bowl and mix well.
Drizzle lamb shoulder with olive oil and rub all over before covering lamb with rub. You can also do this the night before.
Lightly pierce eggplant all over with tip of a sharp knife.
Place lamb and eggplant into smoker, and spritz lamb every 45 minutes.
At 180°F internal temp, wrap the lamb with peach paper or heavy foil.
After around 7 hours, or at between 205-210°F internal temp, your lamb should be ready. It should probe with a skewer like a hot knife through butter. Test in several places as the shoulder won't cook evenly.
Rest your lamb for at least an hour covered in towels in a cool box, then pull into chunks.