Combine corned beef and water to cover in a large Dutch oven; bring to a boil then remove from heat. Drain. Add fresh water to cover. Add onion, carrot, parsley, bay leaf, and pepper. Bring to a boil once again, then reduce to a low simmer. Skim off foam, if necessary. 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.
To make the Irish Mustard Sauce, combine cornstarch, sugar, dry mustard and salt in a medium saucepan; stir well. Add water and cook over low heat, stirring constantly, until thickened. Remove from heat. Stir in vinegar, butter and horseradish. Gradually stir about 1/4 of hot mixture into yolks; add to remaining hot mixture, stirring constantly. Cook over low heat, stirring constantly, until thickened.
Transfer corned beef and vegetables to a serving platter. Serve with Irish Mustard Sauce.