Place the corned beef brisket in a large pot or Dutch oven. Add the water, making sure the brisket is well submerged.
Add the onion, garlic, bay leaves, and peppercorns to the pot. Bring the water to a boil over medium-high heat.
Once boiling, reduce the heat to low, cover the pot, and simmer for about 2.5 hours, or until the corned beef is tender.
After 2.5 hours, add the carrots and potatoes to the pot. Continue to simmer the mixture for an additional 30 minutes.
In the last 10 minutes of cooking, add the cabbage wedges to the pot. Cover and cook until the cabbage is tender.
Once all the ingredients are done, carefully remove the corned beef and let it rest on a cutting board for about 10 minutes before slicing.
Slice the corned beef against the grain and serve on a platter alongside the vegetables. Ladle some of the cooking broth over the entire dish for added flavor.