Preheat grill to Medium-Low, or about 300 degrees F.
Rub brisket with spices. Place in Dutch oven and pour enough water into the Dutch oven to come up about 1/2 an inch from the bottom around the roast. Cover, place on grill, close lid, and grill for 90 minutes.
Add potatoes and carrots to the Dutch oven and cook again in the closed grill for 45 minutes. Then add cabbage, close lid, and grill for 15 minutes.
Let meat rest for 15 minutes, then serve with vegetables and pan juices.
You can also skip the spice rub and use an already-cured corned beef brisket.