Place the onion wedges, peeled carrot chunks, and quartered potatoes in the bottom of a large crock pot.
Unwrap the corned beef brisket and sprinkle the included spice packet over the top, or use 1 tablespoon of pickling spice for extra flavor.
Place the brisket on top of the vegetables, fat side up.
Pour 4 cups of beef broth or water around the sides until it comes up around the meat and vegetables.
Cover and cook on LOW for 7–8 hours (or on HIGH for 4–5 hours), until the beef is fork-tender.
About 1–2 hours before the end of cooking, tuck the cabbage wedges into the liquid around the brisket. Recover and continue cooking until the cabbage is tender-crisp.
When done, carefully transfer the brisket to a cutting board and let rest for 10–15 minutes.
Slice the brisket against the grain into thick pieces.
Serve the sliced beef with the cooked vegetables and a drizzle of the cooking liquid. Offer Dijon mustard or horseradish on the side.