1. Place the corned beef in a large soup kettle or dutch oven. Add the onions, halved carrots, celery, and parsley sprigs. Cover with cold water and bring to a boil. Then reduce the heat, cover, and simmer for 2¾ to 3 hours, turning the beef over in the broth every 30 minutes. When the meat is very tender, remove it from the kettle and keep warm.

2. Strain the broth and return it to the kettle. Add the cabbage, potatoes, leeks, cut-up carrots, salt and pepper, and 2 tablespoons of the chopped parsley. Bring to a boil; reduce the heat, cover, and simmer until the vegetables are tender, 30 minutes.

3. Arrange the beef on a warmed serving platter, and surround it with the cooked vegetables. Ladle broth over the beef and vegetables, and sprinkle with the remaining 2 tablespoons chopped parsley. Serve with the Horseradish Cream Sauce.

For the Sauce:

1. Whip the heavy cream in a bowl until it forms soft peaks.

2. Combine the mayonnaise, horseradish, and mustard in another bowl. Using a rubber spatula, fold in the whipped cream. Add the sugar, salt, and pepper. Stir well, and transfer to a serving bowl. Makes 2 cups