Rinse the brisket and pat dry. Trim the fat cap to approximately 1/4-inch thick and score the fat with a sharp knife, making sure not to cut through to the surface of the meat. Set aside.
Combine the salt, black pepper, green pepper, and white pepper in a small bowl and whisk to combine. Sprinkle the spice mixture over the entire brisket and rub all over. Cover with plastic or foil and refrigerate overnight.
Place 4 ounces of hickory wood chunksMeasuring approximately 2-by-2-by-3 inches. into the smoker box and turn smoker to 225ºF. Place drip pan under smoker.
Unwrap the brisket and place directly on the center rack, fat-side up. Close the door and cook until the brisket reaches an internal temperature of 140 to 150ºF.
Remove the brisket and wrap in a double layer of aluminum foil. Place it in a pan, put it back in the smoker, and continue to cook until the brisket yields to pressure when pressed, is pinkish on the inside, pulls apart easily, the fat cap is slightly blackened and jiggles, and when picked up with two pairs of tongs, bends in half and sags almost as though it will break in half. It should reach an internal temperature of 185 to 190ºF fairly quickly, and then hold that temperature for several hours. Don’t rush this step.
Rest at room temperature for 45 minutes to 1 hour before slicing and serving with a side of bread and butter pickles.