12 hours before smoking, rub the brisket with mustard and dry rub. Wrap in plastic wrap and refrigerate until ready to smoke.
Remove the meat from the refrigerator. Place the wood smoking chips in a bowl of water.
Add lump charcoal to the Big Green Egg, filling to the first line. Tuck a natural charcoal starter into the charcoal and light it. Let it burn for about 10 minutes with the lid open.
Remove the wood chips from the water and sprinkle on top of the coals around the perimeter of the egg.
Add the plate setter into the egg, feet up. Place an aluminum pan on the plate setter and fill with 2 cups apple cider. This will add more moisture to the meat and will collect drippings. Add the grill rack.
Shut the lid and set the temperature for 225-250 degrees F. To do this, leave about one-inch open on the bottom
And a quarter-inch open on the top vent.
Place the brisket on the grill fat side down (that's a pork butt on the left). Close the lid; making sure the top vent is properly set. Smoke for 2 hours, keeping an eye on the temperature.
After 2 hours, flip the brisket over. Close the lid and smoke another 2 hours until it reaches 165 degrees.
Once it reaches 165 degrees, place the brisket fat side up on multiple pieces of foil. Pour about ½-cup of coffee onto the brisket and wrap it up tightly.
Place it back on the smoker. Close the lid and cook to 200 degrees. Remove from smoker and let rest, wrapped for about 30 minutes in a cooler.
Remove from the foil and slice against the grain. Serve with pickles, raw white onions and bread.