Beef shoulder is a lot leaner than brisket, so it requires just the right amount of heat and wood smoke to transform this tough cut into something tender enough to tear apart with your fingers.
Step 1: Place the salt, peppercorns, and cayenne in a small bowl and stir to mix. (Actually, your fingers work better for mixing the rub than a spoon or whisk does.)
Step 2: Generously sprinkle the rub over all sides of the clod, patting it onto the meat with your fingertips.
Step 3: Set up the grill for indirect grilling and preheat to medium-low. If using a gas grill, place 4 cups of the wood chips or chunks in the smoker box or in a smoker pouch and run the grill on high until you see smoke, then reduce the heat to medium-low. If using a charcoal grill, place a large drip pan in the center, preheat the grill to medium-low, then toss 1 1/2 cups of the wood chips or chunks on the coals.
Step 4: When ready to cook, place the clod, fat side up, in the center of the hot grate, over the drip pan and away from the heat. Cover the grill and cook the clod until darkly browned and cooked through, 8 to 9 hours. To test for doneness, use an instant-read meat thermometer: The internal temperature should be between 190° and 195°F for well-done, which is the way clod is usually served. If the outside starts to burn, cover it loosely with aluminum foil. If using a gas grill, every 2 hours you’ll need to add 4 cups of wood chips or chunks. If using a charcoal grill, every hour you’ll need to add 12 fresh coals and 3/4 cup of wood chips or chunks to each side.
Step 4: Transfer the grilled clod to a cutting board and let it rest for 10 to 15 minutes, then thinly slice it across the grain with a sharp knife.