Place potatoes, onion, carrots, celery, and garlic at the bottom of a 6-quart slow cooker.
Lay the corned beef on top, fat side up. Pour in juices from packaging if desired.
Sprinkle included spice packet and any additional pickling spice over the top.
Pour enough beef broth to just barely cover the brisket.
Cover and cook on LOW for about 8–9 hours.
One hour before serving, add the cabbage wedges around the brisket.
Once cooked, remove the brisket and let rest 10 minutes. Slice against the grain or shred.
Serve with the cabbage and vegetables, and optional mustard or horseradish.