In a large slow cooker, place the corned beef on the bottom of the slow cooker (do not rinse off--allow all the juices from the packaging to go inside the slow cooker). Sprinkle pickling spices on top of the corned beef.
Layer with peeled carrots and onions, followed by the baby potatoes. Place sprigs of thyme around the slow cooker then pour the water over the ingredients.
Set on LOW and cook for 8 hours.
Once the corned beef and vegetables have cooked for 8 hours, move around the vegetables to make room for the cabbage.
Submerge the cabbage in as much liquid as possible, place the lid back on the crock pot and place on HIGH for 1 hour.
Slice the Corned Beef against the grain, divide vegetables evenly among plates, and serve with a grainy mustard.