Place potatoes, carrots and onion in 6-quart slow cooker. Place corned beef brisket over vegetables. Sprinkle with pickling spice and minced garlic. Add enough water (about 8 cups) to just cover meat. Cover.
Cook 7 hours on HIGH. Add cabbage. Cover. Cook 1 to 2 hours on HIGH or until cabbage is tender-crisp.
Remove corned beef brisket to serving platter. Slice thinly across the grain. Serve with vegetables.