Preheat your oven to 325°F (160°C).
Rinse the corned beef under cold water and pat dry with paper towels.
In a small bowl, mix together the Dijon mustard and brown sugar until well combined.
Place the quartered onion in the bottom of a large Dutch oven or heavy-bottomed roasting pan.
Position the corned beef on top of the onions, fat side up.
Spread the mustard-sugar mixture evenly over the top of the corned beef.
Sprinkle the minced garlic over and around the meat, then add the contents of the seasoning packet.
Pour the water and Irish stout around (not over) the corned beef. The liquid should come about halfway up the sides of the meat.
Cover the Dutch oven tightly with its lid (or use heavy-duty aluminum foil if using a roasting pan).
Place in the preheated oven and cook undisturbed for 2.5 hours.
While the beef is cooking, prep your vegetables. In a large bowl, toss the quartered potatoes and carrot chunks with the melted butter and horseradish mixture. Season lightly with salt and pepper.
After the beef has cooked for 2.5 hours, carefully remove the Dutch oven from the oven.
Arrange the seasoned potatoes and carrots around the corned beef, then place the cabbage wedges on top of the vegetables and around the sides of the meat.
Cover the pot again and return it to the oven for another 1 hour, until the beef reaches an internal temperature between 190-200°F (88-93°C) and the vegetables are tender.
While the beef and vegetables finish cooking, prepare the horseradish sauce. In a mixing bowl, combine the sour cream, prepared horseradish, Dijon mustard, and mayonnaise (if using).
Add the lemon juice or vinegar and stir until the mixture is smooth and well blended.
Season with salt and freshly ground black pepper to taste.
Cover and refrigerate the horseradish sauce for at least 30 minutes to allow the flavors to meld.
When everything is cooked, transfer the corned beef to a cutting board and tent it loosely with aluminum foil.
Let it rest for 10-15 minutes to allow the juices to redistribute.
Using a sharp knife, slice the corned beef against the grain into thin slices.
Arrange the sliced corned beef on a platter with the vegetables surrounding it.
Sprinkle with freshly chopped parsley if desired.
Serve with the horseradish cream sauce on the side.