Remove brisket from brine and rinse well under cold water. Run the brine solution through a strainer and reserve the pickling spices.
Add the quartered onion and halved garlic head to a large Dutch oven. Set the corned beef on top of that and cover with water by several inches. Add the reserved pickling spice. Set over high heat and bring to a boil. Let it boil for 15 minutes and then reduce to a simmer. Cover and gently simmer for 3 to 4 hours or until the meat is fork tender.
If doing the glaze, preheat broiler. While broiler is preheating, melt the butter in a sauce pan, over medium high heat, and add the brown sugar and water. Once sugar has dissolved, add the mustard and simmer for another couple of minutes. Reserve.
When corned beef is done, remove from the liquid (you can use that liquid to cook cabbage, carrots and potatoes) transfer to a baking sheet and brush glaze all over it. Broil for 20 minutes, brushing more glaze as needed.
Slice corned beef against the grain. Serve with veggies and mustard.