Heat the grill, close the lid, and then allow the grill to come up to 225 degrees Fahrenheit.
Remove any excess fat from the brisket.
Combine the beef broth, salt, and 2 tablespoons of the coffee rub in a bowl.
Place the brisket in a high sided pan or tub and then inject it with the mixture.
Using the remaining coffee rub and salt, coat the exterior of the brisket.
Place the brisket on the grill and allow it to cook for about 6 hours or until the internal temperature reaches 160 degrees Fahrenheit.
Using butcher paper or a double layer of foil, wrap the brisket and then place it back onto the grill for another 3 hours or until the internal temperature reaches 204 degrees Fahrenheit.
Remove the brisket from the grill.
Open one end of the foil or wrap to allow the steam to escape.
Reseal the corner of the wrapping and allow the brisket to rest up to an hour.
Slice and serve.