Combine corned beef and water to cover in a large Dutch oven; bring to a boil. Remove from heat. Drain. Add fresh water to cover. Add onion, carrot, parsley, bay leaf, and pepper. Bring to a boil. Skim off foam, if necessary.
Reduce heat, cover and simmer 4 hours or until tender. Remove onion and parsley. Add potatoes to Dutch oven. Simmer 10 minutes. Add cabbage wedges, and simmer 20 minutes or until vegetables are tender. Remove and discard bay leaf.
Transfer corned beef and vegetables to a serving platter. Serve with Irish Mustard Sauce. Yield: 6-8 servings.
