Prepare your cooker (gas or charcoal grill or barbecue smoker) to cook indirectly at 235°F (113°C), using hickory wood if you have a smoker.
Season the brisket liberally on all sides with the Barbecue Rub #67. Cook the brisket, fat side down, for 1 hour. Then flip it fat side up and cook to an internal temperature of 160°F (71°C), another 3 to 4 hours.
Place 2 very large sheets of heavy-duty aluminum foil, one atop the other, on your work surface, long side facing you. Fold the right half of the foil over the left half, crease, and unfold. Remove the brisket from the cooker and leave the heat on. Place the brisket, fat side up, in the center of the left half of the foil. Turn the edges of the foil up to create a lip and pour the coffee over the brisket. Fold the other half of the foil over the brisket and crimp the edges shut. (Be careful not to pierce the foil. If you do, don’t freak. Just start over, wrapping the brisket in foil all over again.)
Return the foil-wrapped brisket to the cooker until it reaches 200°F (93°C). Begin checking the internal temperature of the brisket after 1 hour. When it’s ready, remove the brisket package from the heat, unwrap it, and let it rest for 30 minutes.
Move the brisket to a cutting board. If desired, reserve the coffee mixture, skimming the fat from the surface of the liquid and serving the remaining juices as a sauce. Slice the brisket on the diagonal into 1/4-inch-thick slices. It's up to you if you want to serve the brisket straight from the cutting board or pile it on a platter.