Remove the pork roast from the brine about 1/2 hour before you will be ready to cook it to allow it to come up to room temperature. When ready to cook, heat a grill to high heat. Dry the pork, rub it with olive oil, and season it with pepper. Sear the pork on all sides to get grill marks. Move the roast to an upper rack (or over indirect heat) and put a drip pan underneath it. Cook the pork until the internal temperature reaches 145 degrees F, about 30 to 45 minutes. Remove to a platter, cover loosely with foil, and allow it to rest for 10 minutes.
Before carving, add any accumulated juices to the drippings in the pan. Spoon these over the sliced pork.