Starting the night before, soak the hickory logs in water. (I use a five gallon bucket from the hardware store.)
Allow the brisket to sit at room temperature for 1 hour. Meanwhile prepare a charcoal grill for indirect heat using lump hardwood charcoal to 225°F-250ºF. Place a drip pan under the grate where the beef will be. Add a hickory log and make sure you have a good smoke before adding the beef.
To prepare the rub, combine the brown sugar, granulated sugar, onion powder, garlic powder, paprika, chili powder, salt, and pepper in a medium bowl. Pat the brisket dry with paper towels. Cover the entire brisket with the mustard. Rub the rub mixture all over, massaging into the skin.
Oil the cooking grates and place the brisket (fat side up!) on the grill and cook until the internal temperature reaches 160°F-165º F (this should take about 3 to 3 ½ hours), rotating (not flipping) the brisket half way through cooking, adding hickory logs as needed and maintaining the temperature of the coals.
Tear off two pieces of heavy-duty aluminum foil that will be large enough to completely wrap the brisket and place over a baking sheet. Remove the brisket from the grill and place, fat side up, on the foil. One sheet at a time, wrap the brisket tightly. Return the wrapped brisket to the grill and cook until the internal temperature reaches 180ºF, about 2 ½ to 3 hours, adding hickory logs as needed and maintaining the temperature of the coals.
Meanwhile, line a small cooler with thick bath towels to insulate the inside of the cooler. Remove the brisket from the grill. Keep the aluminum foil wrap in place and wrap again in plastic wrap. Place the brisket in a baking dish or disposable pan and place it in the cooler. Cover the top of the brisket with another towel, close the lid and allow the meat to rest for 1 hour.
Prepare the grill with a medium fire. Carefully unwrap the brisket, reserving meat juices. Baste the brisket with the sauce and grill on both sides until sauce has caramelized and set, about 5 to 10 minutes per side. Transfer the brisket to a cutting board, lightly tent with aluminum foil, and allow to rest for 20 minutes before slicing.
Meanwhile, de-fat the reserved meat juices. Add 1/2 cup of the meat juices to the barbecue sauce. Serve the sauce warm or at room temperature. Slice the beef against the grain and transfer to a serving platter and serve with the juices and the sauce. Enjoy!