Rinse the corned beef and place in a large crock pot with all of the vegetables.
Combine the apple juice, brown sugar, and mustard in a bowl and then pour over the meat and vegetables.
Cook on high heat for 4 to 5 hours, or on low heat for 8 to 10 hours, until the meat is tender. Remove the meat to a cutting board and slice thinly against the grain. Serve with the vegetables and the broth.