Step 1: Prepare the Corned Beef. Remove the corned beef from its packaging. Rinse it thoroughly under cold running water for several minutes to remove excess brine. Pat it dry with paper towels.
Step 2: Add to Slow Cooker. Place the rinsed corned beef brisket, fat-side up, into your slow cooker. Adding it fat-side up allows the fat to render and baste the meat as it cooks, keeping it incredibly moist.
Step 3: Add Spices and Liquid. Sprinkle the pickling spice packet (and any additional spices like extra bay leaves or peppercorns, if using) over the corned beef. Pour in enough water, beef broth, or even a stout beer (like Guinness) to cover about two-thirds of the meat. A general guideline is about 4-6 cups of liquid for a 3-4 pound brisket.
Step 4: Cook the Beef. Cover the slow cooker and cook on LOW for 6-8 hours or on HIGH for 3-4 hours, until the corned beef is fork-tender. The exact time will depend on your slow cooker and the size of your brisket. The meat should be easily pierced with a fork.
Step 5: Add Vegetables. About 2-3 hours before the end of the cooking time (if cooking on LOW) or 1 hour before (if cooking on HIGH), add the potatoes and carrots to the slow cooker, pushing them down into the liquid.
Step 6: Add Cabbage. About 30-45 minutes before serving, add the cabbage wedges to the slow cooker, arranging them on top of the meat and other vegetables. Cook until the cabbage is tender but still has a slight bite.
Step 7: Rest, Slice, and Serve. Carefully remove the corned beef from the slow cooker and transfer it to a cutting board. Tent it loosely with foil and let it rest for 10-15 minutes. This allows the juices to redistribute, resulting in a more tender and flavorful slice. While the meat rests, you can remove the vegetables from the slow cooker and keep them warm. Slice the corned beef against the grain for maximum tenderness. Serve immediately with the cooked vegetables and a drizzle of the flavorful cooking liquid.