Gather all ingredients. Rinse brisket under cold water and place in a large pot. Add enough water to cover roast by 6 inches. Peel onions and place them in the pot. Bring to a boil; cook for about 30 minutes at a rolling boil. Reduce heat to medium-low, so water is at a gentle boil. Cover and cook for 3 1/2 hours. Remove onions and cut them into wedges. Return them to the pot. Add carrots to the pot, then place cabbage over roast. Place potatoes on top of cabbage. Cover and cook for 30 more minutes until potatoes are tender. Remove vegetables from the pot and place in a separate serving bowl. Keep corned beef in the pot until ready to slice and serve to avoid dryness.