Combine the ingredients for the brine and bring to a simmer in a stock pot. After the mix boils, chill completely, then immerse the lamb in the brine and weight it down in a container large enough to fit the ham. Keep the shoulder in the brine for 5 days, then remove.
Smoking
Transfer the lamb to a 250F smoker for 2-2.5 hours or until it reaches an internal temperature of 150F. From here, the ham can be chilled until the day it will be served, and will keep refrigerated for 5 days.
To make slicing easier, cut the whole muscles off the bone.
To serve, using a sharp, long knife, cut thin slices of the pastrami. Heat the pastrami in a pan for sandwiches, serving alongside eggs, or whatever else you like.
Notes
Lamb or goat shoulder can be smoked just like a ham, but will have slightly more fat.