Take brisket out of package and wash slime. Place in a pot and add cold water to cover brisket. Add the season packet to the pot. Turn on high and bring to a boil, flipping brisket over halfway through cooking if necessary. Set timer for 30 minutes.
Carefully remove brisket from pot to a baking sheet (I suggest covering with foil for easier clean up) and pat dry, smother the whole brisket with the mustard/honey/brown sugar paste and put into a preheated oven of 375*F bake for 20 minutes. Turning over and basting again with glaze mixture.
While the brisket is baking, place prepared vegetables in the pot in this order, potatoes, carrots, celery, onions and cabbage. cover and bring to another boil. Remove everything that has just softened ie cabbage, onions, celery and carrots, approx 10 minutes (no mushy vegetables!) and let potatoes continue to boil until a knife goes through easily. Drain and arrange on your platter. The salt from the corn beef will slightly season the vegetables and not over power them. Be sure to cover with foil to keep them warm.
When the timer for the baking goes off, remove brisket from oven, slice....yes, slice into serving pieces but I have found in my attempts to make this that having that caramelized glaze on the meat makes it out of this world. So slice the meat and place back on the baking sheet, drizzle with the glaze and this time broil for 10 minutes or just when you see the caramelizing happening. DON"T BURN! Remove sliced brisket from baking sheet and move to the center of your platter among those yummy vegetables! Enjoy with a loaf of Irish Soda or sourdough bread.