Place the halved baby gold potatoes in the bottom of the slow cooker.
Add the carrot chunks and onion wedges over the potatoes.
Place the corned beef brisket on top of the vegetables, fat side up.
Sprinkle the spice packet evenly over the top of the corned beef.
Add the minced garlic over the meat.
Pour the beef broth or water around the sides of the corned beef, not directly over the top.
Cover and cook on low for 6 to 7 hours or on high for 4 hours, until the corned beef is fork tender.
About 60 minutes before serving, tuck the cabbage wedges into the slow cooker around the meat.
Cover and continue cooking until the cabbage is soft and translucent.
Remove the corned beef from the slow cooker and let it rest for 5 minutes.
Slice the corned beef against the grain into thick slices.
Serve the sliced corned beef with the potatoes, carrots, cabbage, and spoon some of the cooking broth over the top.