Step 1: Remove the corned beef brisket from its packaging and rinse thoroughly under cold water to remove excess salt. Pat dry with paper towels.
Step 2: Place the rinsed corned beef brisket into the bottom of a large slow cooker (6-quart or larger). If a spice packet was included, sprinkle its contents over the brisket. If not, add 1 tablespoon of pickling spice, 1 teaspoon of black peppercorns, and 1-2 bay leaves.
Step 3: Arrange the quartered onion, halved or quartered potatoes, and carrot chunks around the corned beef in the slow cooker.
Step 4: Pour the beef broth or dark beer over the meat and vegetables. Ensure the liquid comes at least halfway up the sides of the brisket.
Step 5: Cover the slow cooker and cook on the LOW setting for 7-8 hours, or on the HIGH setting for 3-4 hours, until the corned beef is fork-tender.
Step 6: About 1 hour before the end of the cooking time, add the cabbage wedges to the slow cooker. Gently nestle them into the liquid and around the meat and other vegetables.
Step 7: Once cooking is complete and the corned beef is very tender, carefully remove the brisket from the slow cooker and transfer it to a cutting board. Tent loosely with foil and let it rest for 10-15 minutes.
Step 8: While the meat rests, remove the vegetables from the slow cooker with a slotted spoon and keep warm.
Step 9: Slice the corned beef against the grain into desired thickness. Serve immediately with the cooked vegetables and a side of Dijon or whole grain mustard.