In a small bowl mix the rub ingredients. Press the mixture into the surface of the roast, cover with plastic wrap and refrigerate for 3 hours or as long as 24 hours. Allow the roast to stand at room temperature for 15 to 30 minutes before grilling.
Soak the wood chips in water for at least 30 minutes.
Prepare the grill for indirect cooking over medium heat (180°C to 230°C).
Brush the cooking grates clean. Drain and add the wood chips to the charcoal or to the smoker box of a gas grill, following the manufacturer’s instructions. When the wood begins to smoke, sear the roast over direct heat, with the lid closed, until both sides are nicely browned, about 5 minutes, turning once. Slide the roast over indirect medium heat, close the lid, and continue cooking to your desired doneness, 20 to 30 minutes for medium rare. Remove from the grill and let rest for 3 to 5 minutes. Cut the roast against the grain into thin slices.
Build each sandwich between two slices of bread with meat and a dollop of sauce. Serve warm or at room temperature.
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