01 - Rinse the corned beef thoroughly under cold running water to remove excess brine. Place the brisket in the slow cooker with the fat side facing up.
02 - Sprinkle the entire contents of the spice packet evenly over the brisket. Add the Dijon mustard at this stage if you prefer an extra layer of flavor.
03 - Arrange the onion quarters, smashed garlic cloves, carrot chunks, and halved potatoes around and on top of the meat. Tuck in the bay leaves and scatter the peppercorns throughout.
04 - Pour the beef broth and water evenly over all the ingredients in the slow cooker, ensuring everything is partially submerged.
05 - Cover the slow cooker with its lid. Cook on LOW setting for 8 hours, or until the meat is fork-tender and easily pulls apart.
06 - Gently nestle the cabbage wedges into the cooking liquid during the final 2 hours of the slow cooking process. Cover and continue cooking until the cabbage is tender but not mushy.
07 - Carefully lift the corned beef from the slow cooker using tongs and transfer it to a cutting board. Let the meat rest for 10 minutes before slicing thinly against the grain for maximum tenderness.
08 - Arrange sliced corned beef on plates alongside the tender vegetables. Spoon some of the flavorful cooking broth over the top for added moisture and richness.