Rinse the corned beef in cold water. Trim any excess fat leaving about ¼-inch.
Add water to the slow cooker and turn on high. Add the bay leaves, thyme sprigs, black pepper and brown sugar. Stir to dissolve the sugar. Carefully place the corned beef into the slow cooker, fat side up. The roast should be covered by the water. Sprinkle the pickling spices over the beef. Cover and cook on high for 2 hours.
Remove the lid from the slow-cooker and carefully add the onions, potatoes and carrots, placing them between the beef and the side of the slow cooker. Cover and continue cooking on high for 3 more hours.
Cut the cabbage through the core into 4 (2-inch thick) wedges. Leave the core intact so the wedges don’t fall apart during cooking. Place the cabbage wedges on top of the corned beef and vegetables. The slow cooker will be full at this point. Cover and continue cooking for another 1 to 2 hours, or until the corned beef and vegetable are tender.
The corned beef should be cooked for a total of 6 to 7 hours on high, or 8 to 9 hours on low, depending on the thickness of the brisket.
Remove the brisket from the slow cooker to a cutting board, and tent with foil. Allow the roast to rest for 15 minutes before slicing.
Slice the brisket thin, against the grain, and place on a serving platter. Remove the vegetables from the slow cooker using a slotted spoon and arrange on the platter around the corned beef. Drizzle the vegetables with melted butter, if desired.
Serve with plenty of fresh ground black pepper, a hunk of bread and a dollop of creamy mustard sauce.