Roughly chop the cabbage and place it in the slow cooker with the carrots. Place the corned beef on top and fill the slow cooker with water until the corned beef is covered. If you want, you can add beer or stock. Cook on low for 7-8 hours.

Remove the corned beef and let it rest for 10 minutes. Then slice it against the grain, as you would slice a good steak. Serve the sliced corned beef with the cabbage and carrots.