Step 1: Rinse the corned beef brisket thoroughly under cold water to remove any excess salt. Pat it dry with paper towels.
Step 2: Place the rinsed corned beef brisket, fat-side up, into the bottom of a large slow cooker (6-quart or larger).
Step 3: Sprinkle the contents of the spice packet over the brisket. If you don't have a spice packet, use 1 tablespoon of pickling spice.
Step 4: Pour the water or beef broth into the slow cooker, ensuring the liquid almost covers the brisket. If using, add the dark beer or apple cider vinegar and bay leaf now.
Step 5: Add the chopped onion, carrots, and potatoes around the corned beef in the slow cooker.
Step 6: Cover and cook on LOW for 6-8 hours, or on HIGH for 3-4 hours, until the corned beef is fork-tender. Cooking time will vary depending on your slow cooker and the size of your brisket.
Step 7: Approximately 1 hour before the end of the cooking time, add the cabbage wedges to the slow cooker. Arrange them around the meat and other vegetables, pushing them gently into the liquid.
Step 8: Continue cooking until the cabbage is tender but still has a slight bite, usually about 45-60 minutes.
Step 9: Carefully remove the corned beef from the slow cooker and transfer it to a cutting board. Tent loosely with foil and let it rest for 10-15 minutes.
Step 10: While the beef rests, transfer the cooked vegetables and cabbage to a large serving platter. You can skim any excess fat from the cooking liquid if desired.
Step 11: Slice the rested corned beef against the grain into desired thickness. Arrange the sliced corned beef with the vegetables on the serving platter.
Step 12: Serve hot, drizzled with some of the cooking liquid, and with Dijon mustard on the side. Garnish with fresh parsley if desired.