Rinse the corped beef brisket and place it in a large pot or Dutch oven.
Add minced garlic, cayenne pepper, and black pepper to the pot with the corned beef.
Fill the pot with enough water to cover the brisket by at least an inch. Bring to abboil, then reduce heat and simmer, covered, for about 2.5 to 3 hours until fork-tender.
Add cabbage wedges to the pot about 30 minutes before the corned beef is done.
Once everything is cooked, remove the corned beef and let it rest before slicing it against the grain.
Serve the sliced corned beef with the cooked cabbage.