Place the chopped onion and minced garlic at the bottom of the Crock Pot.
Rinse the corned beef brisket under cold water to remove excess salt and place it on top of the onions and garlic.
Sprinkle the spice packet that came with the corned beef over the meat.
Add the carrots around the brisket, then pour in the beef broth.
Add the black pepper, dried thyme, and bay leaves.
Cover and cook on low for 8 to 10 hours or on high for 4 to 5 hours, until the meat is tender.
About 1 hour before serving, add the cabbage wedges on top of the corned beef and carrots, cover, and continue cooking.
Once done, remove the corned beef from the pot and let it rest for 10 minutes before slicing against the grain.
Serve the sliced corned beef with the cooked vegetables and broth.