Place the corned beef in a large dutch oven, along with the contents of the spice packet included in the corned beef, brown sugar, bay leaves, onion, and garlic. Fill with enough cold water to cover the beef. Bring to a boil over high heat, lower the flame, cover and simmer for 2 hours or until the beef is tender.
Use a slotted spoon to remove and discard the onions and garlic (they’ve done their job and have given all their flavor already).
Peel the potatoes, I use red potatoes and peel only the center because I like the look of it, but feel free to peel all of it or don’t peel at all. Cut the carrots into large chunks. Place the potatoes and carrots into the pot with the brisket. Return to a boil over high heat and then reduce heat and simmer until fork tender, about 30 to 40 minutes. It depends on how big your potatoes are.
Transfer the potatoes and carrots to a platter and keep warm. Add in the sliced cabbage, I like to keep the core in the cabbage so that the sliced wedges stay in tact, making it easier to move later. Bring back up to a boil over high heat. Lower the flame and simmer for 15 minutes until the cabbage is tender as well.
Transfer the cabbage to the platter along with the potatoes and carrots and move the brisket to a cutting board. Cover loosely with foil and allow to rest for 10 minutes before thinly slicing against the grain. Arrange the sliced beef along with the vegetables on the platter. Sprinkle with parsley and serve with grainy mustard and horseradish sauce (recipe follows).
To make the sauce, set a medium saucepan over moderate heat with the butter. Once melted, whisk in the flour and cook for about 30 seconds or so. Slowly whisk in 1 cup of the liquid that the beef cooked inches Cook, stirring often, until thickened, about 10 to 12 minutes. Stir in the sugar, vinegar, horseradish, salt and pepper.