Combine ingredients for spice rub in a large resealable bag.

Add meat to the bag and rub on all sides with spice rub. Marinate in the refrigerator for at least one hour or up to 24 hours.

Remove meat from refrigerator and let stand while preheating broiler or grill. If broiling, spray broiling pan with nonstick cooking spray and line bottom tray with foil.

Transfer meat to prepared pan; spread barbecue sauce over the top. Broil or grill for eight to 10 minutes per side or until meat reaches desired doneness. (For medium, cook to 145 degrees Fahrenheit.)

Let meat rest for five minutes. Slice against the grain, on the diagonal, into thin slices. Transfer to a serving platter. Serve hot or cold.