Brisket is the fatty, fibrous cut of meat behind the foreshank and below the chuck. The second cut of the brisket, toward the shoulder, is the cut most often preferred for corned beef and for grilling. Note that when grilling brisket, it has to be precooked for several hours before it is grilled. Here, we parboil it and when it is tender, rub it with a dry rub, allow it to marinate in its own juices, and then finish it on the grill.