In a large Dutch oven, place brisket, the seasoning packet, brown sugar and bay leaves, in and cover with water. Bring to a boil. Reduce heat; simmer, covered, for 2 hours.
Add potatoes, carrots, and chopped onions; return to a boil. Reduce heat; simmer, covered, just until beef and vegetables are tender, 30-40 minutes. (If pot is full, remove potatoes and carrots before adding cabbage; reheat before serving:)
Add cabbage to pot; return to a boil. Reduce heat; simmer, covered, until cabbage is tender, about 15 minutes. Remove vegetables and corned beef; keep warm.
Slice and serve with vegetables and Mustard Aioli Sauce. Garnish with fresh chopped parsley!