Rinse the corned beef under cold water, pat it dry and place it fat-side up in a 6-quart slow cooker.
Arrange the onion, potatoes and carrots around the brisket and sprinkle the spice packet over the meat.
Add the water and mustard, cover and cook on low for 6 1/2 hours.
Tuck the cabbage wedges around the brisket, cover again and cook until the cabbage is tender and the beef yields to a fork, 1 1/2 to 2 hours more.
Transfer the corned beef to a board and rest it for 15 minutes.
Lift the vegetables to a platter and moisten them with 1/2 cup strained cooking liquid.
Slice the brisket thinly across the grain and serve it with the cabbage, potatoes, carrots and mustardy broth.