Before cooking, remove your corned beef from the brine and rinse any excess liquid from the surface of the roast. Start up your smoker and shoot for a temperature around 250 degrees F. Place the roast on your grill, close the lid and smoke for 3 hours.
While the roast is smoking, prepare the vegetable and braising liquid. Place the onions and carrots in the bottom of a heavy dutch oven pot. Position the cabbage quarters on top of the carrots and onions. Pour the beef broth over the vegetables and sprinkle with the pickling spice seasoning packet.
After the roast has smoked for 3 hours remove it from the grill and place it on top of the vegetables. Sprinkle the roast with additional pickling spice, if desired. Cover the dutch oven with a lid and return to the grill or oven with the temperature set at 250 degrees F. Braise for 4-5 hours or until the internal temperature of the roast is 205-210 degrees F.
During the last two hours of braising, add in 1 1/2 pounds of washed and cubed potatoes or whole fingerling potatoes to the braising liquid.