In a 5-to 6-quart slow cooker, arrange the carrots on the bottom then place the corned beef (fat side up) on top of the carrots. Add enough water to just cover the meat, then add the pickling spices.
Add the lid then cook the corned beef on LOW for 8 hours or on HIGH for 4 hours.
Cut the cabbage into eight wedges then add it to the slow cooker, cover it and continue cooking until the cabbage is tender, about 1 hour on LOW or 30 minutes on HIGH.
Remove the cabbage, corned beef and carrots from the slow cooker.
Slice the corned beef against the grain and serve.
Notes
Use a sharp boning knife to trim as much of the excess fat as possible, which will make the finished dish less oily.
If your brisket came with an included seasoning packet, add it to the cooking liquid along with the 2 teaspoons of pickling spice.
You may need to remove some of the water with a ladle if the cabbage doesn't fit.
When cutting the corned beef, slice against the grain, or perpendicular to the long fibers of the meat.
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