Prepare and heat a grill stocked with hickory. This is a slow cooking meat, so the temperature of the grill should be between 240 and 250 degrees F.
Trim the fat off of the meat, leaving 1/4-inch of fat cover. Season the meat with salt and pepper and grill until an inserted instant read meat thermometer says 200 degrees F in the thickest part of the meat, 12 or more hours, checking the internal temperature every 30 minutes during the last 4 hours. If the brisket seems to dry out, when it reaches an internal temperature of 170 degrees, cook the meat for the remainder of time wrapped in foil.
Wrap the meat in aluminum foil when done cooking and place in a cooler for 3 to 4 hours prior to slicing.
Prior to cutting/slicing, brush the meat with barbecue sauce over the outside surface; serve the meat with more sauce.