In a very large pot, place corned beef and sprinkle seasoning packet over the top. Add the halved onion, carrots, celery and parsley. Cover with plenty of cold water and bring to a boil. Skim off any scummy foam as it appears, reduce heat to a simmer and cover. Simmer for 2½ to 3 hours until very tender, flipping brisket occasionally and skimming foam as necessary. When done, remove to a cutting board and cover with foil to keep warm. While corned beef is cooking, prep your vegetables and make horseradish sauce.
Strain the cooking broth and return to the pot. Add the vegetables -- cabbage wedges, potatoes, carrots, parsnips, leeks and red onion wedges -- and some salt and pepper, and a tablespoon or two of chopped parsley. Bring to a boil, then turn down to a simmer, cover and cook until all veggies are tender. About 20 to 30 minutes, you just have to check a few.
To serve, slice corned beef and arrange in center of large platter. Surround with vegetables, preferably grouped together by type, it's more pleasing to the eye and easier for guests to choose what they want. Ladle some cooking broth over meat and vegetables. Sprinkle with remaining chopped parsley and serve with horseradish cream sauce on the side.
To make horseradish cream sauce: Whip heavy cream until soft peaks form. In a separate bowl, combine mayo, horseradish and mustard. With a spatula, fold in the whipped cream until combined. Add a pinch of sugar and salt and pepper to taste. Transfer to serving bowl and refrigerate until ready to serve.