Trim the fat from the brisket. Combine seasoning in a small bowl to create the BBQ rub and rub it into the brisket on all sides. Allow the brisket to rest and come to room temperature for 1 hour before you start smoking it.
Remove the brisket. Wrap with butcher paper and return to the smoker. Continue smoking the brisket until it has reached an internal temperature of 205°F. This took 7 hours for us, but time may vary.
Place any leftover smoked beef brisket in an airtight container or tightly wrap them up. Then store them in the refrigerator for 3 to 4 days.