The day before cooking, cover the meat with the dry rub, massaging it into the brisket. Wrap in plastic wrap, put in a plastic bag and refrigerate overnight.
The next morning, take brisket out, preheat oven to 275 degrees.
Prepare your grill for indirect heat cooking.
Place brisket fat side up on the unheated side of your grill. You should have a temperature around 250 degrees. If you have a smoker box, use it with hickory chips for three cycles of smoke. If you don't, don't worry about it.
Let the brisket cook on indirect heat for three hours.
Make a foil packet big enough for the brisket. After three hours, place brisket in the packet and pour in the braising liquid. Seal the foil packet and put brisket on a baking dish or pan.
Place in oven, and forget about it for 5 hours.
Check internal temperature every half hour after 5 hours. You want the center of the brisket to be around 190 degrees.
Remove from oven, carefully pour braising liquid into a pan, and bring to a boil. Meanwhile, cover the brisket and let sit. You can turn off the oven and put the brisket back in after 15 minutes.
Let the liquid boil down to a thick consistency. less than half of the original amount should remain.
Slice brisket against the grain and drizzle sauce on top.