Preheat oven to 170 degrees. Remove corned beef from package and rinse well. Place in a roasting pan and cover ¾ with hot water. Sprinkle with spice package that comes with corned beef, add balsamic vinegar, cover tightly and place in oven for 18 to 24 hours.
An hour and a half before serving prepare potatoes, cover with water and boil for about 30 minutes or until slightly tender. Remove from water, season with salt and pepper, and place uncovered in a baking dish in same oven with corned beef.
Heat olive oil in a large skillet, place onions in skillet and sauté slowly until well caramelized, about 30 minutes.
Remove the corned beef from oven; pour off the excess liquid in the roasting pan into a large pot. Return the corned beef to the roasting pan cover and return to oven. Place the cabbage in the liquid in the pot, cover and cook until tender, about 20 to 30 minutes.
When cabbage is done arrange the corned beef, potatoes, onions, and cabbage on a large platter and serve with the mustard.
Optional Slow Cooker Method:
Place brisket in the slow cooker, fat side up. Cover brisket 3/4 of the way with water. Put in 1 cup Balsamic vinegar. Sprinkle brisket with seasoning packet from the brisket. Cover and cook on low for 10-20 hours. (The longer it cooks, the more it dissolves in your mouth.)