Place the sliced onion and minced garlic in the bottom of a slow cooker.
Rinse the corned beef brisket under cold water to remove excess salt and place it on top of the onions and garlic.
In a bowl, mix together the beef broth, Worcestershire sauce, black pepper, paprika, cayenne pepper (if using), brown sugar, and apple cider vinegar. Pour this mixture over the brisket.
Cover and cook on low for 8 to 10 hours or until the meat is tender.
About 1 hour before serving, add the baby carrots and halved potatoes to the slow cooker.
In the last 30 minutes, add the cabbage wedges on top of the vegetables.
Once cooked, remove the brisket and let it rest for 10 minutes before slicing against the grain.
Serve the sliced corned beef with the vegetables and some of the cooking liquid drizzled over the top.