Remove the brisket from the brine and cover it in a pot with cold water. Place it back in the fridge for at least 8 hours. If you are in a rush you can just wash the brisket under cold water for a few minutes but it may still be quite salty.
Spread a thin layer of yellow mustard over the brisket and sprinkle the rub all over it. Use your hand to press the rub in. For a whole brisket flat I used the entire batch of rub.
Fire up your smoker to 250°F and add 2-3 fist size chunks of smoke wood. Apple or cherry work well.
Place the brisket on the smoker, fat side up, and smoke until the internal temperature hits 155 - 160°F. This should take around 5 hours.
Once the brisket has developed a nice mahogany red bark, wrap it tightly in foil and increase the smoker temperature to 300°F.
Continue smoking until the Pastrami feels tender when probed and has an internal temperature between 203 - 207°F.
Take the Pastrami off the smoker and leave it to rest for at least half an hour. Slice thinly and serve.