Preheat your barbecue to medium-high. Place the pepper and salt on a large plate. Brush the roast with olive oil. Roll the roast in the pepper and salt to coat. Set the beef on one side of the barbecue and sear on all sides. Close the lid and turn the heat off underneath the roast; leave the other side of the barbecue set to medium-high. Cook the beef until rare to medium rare, about 30 to 35 minutes, or until the centre of the meat registers 125 degrees F to 130 degrees F on an instant-read meat thermometer. (The time required to get to this temperature can vary depending on the thickness of your roast.)
Glaze the roast with hot barbecue sauce, set on a plate, tent with foil and rest 10 minutes before thinly slicing.
Note: Eye of round roasts, coated in coarsely cracked black pepper, are sometimes available in the meat department. If you find one, make sure to brush the roast with oil to prevent sticking, and then season it with salt.