Remove the brisket from the package, reserving the seasoning packet. Rinse the meat under cool water and pat dry with paper towels. Trim any excess fat from the meat, leaving a thin layer.
Place the brisket in the slow cooker fat side up and sprinkle the top with the reserved seasoning packet.
Nestle the potatoes and carrots around the brisket and pour in the water or beef broth.
Cover and cook on LOW for 6 hours.
After 6 hours, lay the cabbage wedges on top of the brisket and continue cooking on LOW 2 more hours.
Remove the cabbage to a bowl. Dot the cabbage with pats of butter and season with freshly ground black pepper, if desired.
Transfer the brisket to a cutting board and let rest for 5 minutes before slicing and serving.
Notes
Always slice the meat diagonally against the grain.
Serve the corned beef brisket with a side of grainy mustard or horseradish, if desired.
Rinse the meat and discard the extra liquid in the the packaging to remove excess salt.
Cooking the corned beef fat side up adds more flavor and tenderness to the meat.
Although corned beef can be cooked for a shorter time on the slow cooker's HIGH setting, cooking on the LOW setting for a longer time will result in a better texture and tenderness.
You may use low-sodium beef broth in place of water.