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Make the mop sauce: Combine the coffee, beer, brown sugar, chile powder and garlic salt in a bowl and whisk to dissolve any salt or sugar crystals. Transfer to a clean spray bottle and set aside.
In a small bowl, mix the Prime Rib Rub and the ground coffee. Rub this mixture on the brisket, covering all surfaces.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes).
Put the brisket directly on the grill grate and smoke for 2 hours. Spray the brisket with the mop sauce and transfer to an aluminum foil pan.
Increase the temperature to 275F and continue to cook for 4 to 5 hours, spraying every hour with the mop sauce. If at any point the brisket appears to be drying out, cover it tightly with aluminum foil. (Discontinue mopping if you do this.) When done, the internal temperature of the brisket will be 185 to 190F (anything less, and your brisket will be tough).
Let rest for 15 to 20 minutes before carving across the grain into 1/4-inch thick slices. Serve, if desired, with barbecue sauce on the side.