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 whole-medium red potatoes.
Place sprigs of thyme around the slow cooker then pour the beer and water over the ingredients.
Set on low and cook for 7 hours.
Once the corned beef and vegetables have cooked for 7 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 and serve with a grainy mustard.
Notes
You know your slow cooker best. Depending on slow cooker brands your cabbage may need to cook longer. Don't serve raw cabbage - it's just wrong. Nor should you serve soggy, over-cooked cabbage. Keep an eye on your slow cooker. To prevent under and over cooking I suggest you check your cabbage at the 30 minute mark. If you don't feel comfortable cooking your cabbage in the slow cooker, simply boil it on the stove top for about 20 minutes or until it is cooked to your liking.
My slow cooker is a KitchenAid 6.5 Quart Oval. Please make sure you are using a slow cooker of at least this size and shape for the recipe.