Apple and Brown Sugar Corned Beef

1 corned beef brisket
1 quart apple juice
1 cup brown sugar
1 tablespoon prepared mustard
8 small red potatoes
2 medium carrots -- pared, and cut into chunks
1 onion -- peeled, and cut into eighths
1/2 cabbage head -- cut into chunks

Place all ingredients in a large slow cooker (cut meat in half if necessary); stir to mix. Cook on HIGH for 4 to 5 hours or on LOW for 8 to 10 hours. Remove meat and vegetables and some of the cooking liquid. Slice meat thinly across the grain. Serve with vegetables and some of the liquid.