Start a natural-wood charcoal fire in your pit, with all the charcoal on one side of the grate. If you're using wood chips (which you will have to if using gas), wrap them in heavy aluminum foil and punch a few holes in the resulting packet. (No need to soak them.)
Trim the brisket of the really thick slabs of fat, but don't be too aggressive--you should never cut into the lean. Don't worry about the fat in the middle, if there is some.
Mix two parts Creole seasoning with one part salt. (For the big brisket, this will be about 1/4 cup seasoning with 2 Tbs. salt.)
Coat the outside of the brisket liberally with the seasoning.
Place the meat on the grill fatty side up, with the thicker end facing the fire, as far away from the heat source as possible. To keep direct heat from the fire from hitting the meat, hang a curtain of aluminum foil between the two. Close the lid and maintain a 225-to-250-degree temperature inside, adding coals and wood now and then. There is no need to turn the brisket, but you might move it around on the grill so the bottom is more evenly smoked.
The brisket is done when the internal temperature, measured with a meat thermometer, hits 165 degrees. This takes three to five hours, depending on the size of the brisket and the heat in your grill.
Let the brisket rest for about 20 minutes before slicing. Whatever fat remains can easily be removed before slicing. Slice against the grain of the meat for easy, tender eating. Note that the direction of the grain changes as you cut; change with it.
