This is my husbands very favorite dinner. When my mother passed about 24 years ago, a wonderful, southern-cook friend of my mom's brought this dish to my father's house. Everyone just raved over it and we've enjoyed it ever since.
Place beef brisket (I have also used corned beef brisket) in a large lidded pot and cover with water. Add the onion, carrot, celery, garlic and peppercorns to pot. Bring water to boil and then reduce heat to simmer and cover pot with lid. Allow to simmer for three hours. Meat is done when it fork-tests tender. When done, remove meat from pot and allow to rest as you prepare the glaze. Set pot aside.
Mix the brown sugar, mustard, ketchup and broth in a small bowl until well combined.
Place meat on cutting board and slice thin against the grain. Lay the meat accordion style into a baking pan with sides. Spread the glaze on top and between the slices of meat. My family really likes the flavor of the glaze and I generally double the glaze mix to generously spread on meat.
Bake at 350 degrees for 20 minutes uncovered until glaze is nice and hot. Discard water and everything else in the pot. I always serve this with potatos, either mashed or baked, and a vegetable. Enjoy!