Trim the excess fat off the brisket. You want to remove most of the fat cap if you have a point or packer cut. Other excess fat should be removed to 1/3 or 1/4 inch until you can see the beef through the fat.
Completely cover the brisket in BBQ rub.
Cover the meat and refrigerate it for 10-12 hours.
Preheat the smoker to 250 degrees F.
Insert a meat thermometer (into the meat, not fat) and place the meat in the smoker until the internal temperature reaches 170 degrees F. This may take 4-5 hours.
Once the meat reaches 170 degrees F, remove the meat and wrap it in foil or peach butcher paper. Place the meat back in the smoker until it reaches 190 degrees F. This make take up to 8 hours.
Remove the meat from the smoker, take the meat out of the wrapping and let it rest for 15 minutes.
Cut up the meat into 1/2 inch cubes.
Coat the cubes of meat with a mixture of 1/2 cup BBQ sauce and all of the pan drippings. It should be enough to completely coat the burnt ends. Use more BBQ sauce if needed.
Place the cubes uncovered into the smoker and cook for 45 minutes. Leave the temperature at 250 degrees F or bump up the temperature to 275 degrees F for a darker coating.
Remove the burnt ends from the smoker and serve.