Place the chopped onion and minced garlic in the bottom of the Crock-Pot.
Add the corned beef brisket on top of the onion and garlic, and sprinkle the spice packet over the meat.
Arrange the carrots and potatoes around the brisket in the Crock-Pot.
Pour the beef broth and Worcestershire sauce over the ingredients, then add black pepper.
Cover and cook on low for 8 to 10 hours or on high for 4 to 5 hours, until the corned beef is tender.
About 30 minutes before serving, add the cabbage wedges to the pot, making sure they are submerged in the broth.
Once everything is cooked, remove the corned beef and let it rest for 10 minutes before slicing against the grain.
Serve the sliced corned beef with the vegetables and broth.