Prepare brisket by removing all but about 1/8 to 1/4 inch of fat on all sides of the brisket. Liberally sprinkle salt and pepper all over the brisket rub in thoroughly. Place the brisket on a wire rack over a sheet pan and refrigerate for 12 hours or overnight. Leave uncovered to allow air to circulate around the brisket, creating a dry surface for better smoke penetration.
Remove brisket from the refrigerator and allow it to come to room temperature, uncovered for about one hour.
Crank up your smoker to 235°F.
Place the brisket fat side up in the smoker and allow to smoke for about 6 hours. When the brisket reaches an internal temperature of 165°F, wrap the brisket in pink butcher paper or tin foil. Continue to smoke for another 4 to 6 hours or until the internal temperature reaches 200°F to 205°F. Remove meat from the smoker to a cutting board and allow to rest for at least an hour before slicing.
Slice brisket across the grain. You will have to pay attention as the brisket grains run different directions throughout.
To store, wrap sliced brisket in tin foil and refrigerate up to 7 days, or freeze in freezer safe bags for up to 6 months.
To reheat brisket, brush olive oil over the sliced meat and wrap in tin foil. Place in a 350°F oven for about 10 minutes or until just warmed, not hot. Do not overcook.