Brisket comes in two different cuts: point and the leaner flat. Depending on which you get, your corned beef may be tender and sliceable (flat cut) or very tender and falling apart (point cut). If your meat isn't labeled, speak with the butcher about which variety your grocery store stocks.
Layer the potatoes, carrots, onions, celery and thyme in the insert of a 6-quart slow cooker. Put the brisket on top of the vegetables and add the beer and pickling spice. Add enough water to just cover the brisket. Cover and cook on low until the meat and vegetables are tender, about 8 hours.
Arrange the cabbage over the brisket (it's OK if the cooker seems crowded), cover and cook until soft and wilted, 45 minutes to 1 hour more.
Whisk together the sour cream, horseradish and mustard in a small bowl.
Remove the cabbage and toss with 1 tablespoon of the butter and pepper to taste in a large bowl. Remove the meat and let rest. Strain the remaining vegetables (reserve some of the cooking broth to serve on the side if you like) and toss with the parsley, the remaining 2 tablespoons butter and salt and pepper to taste.
Slice the corned beef against the grain and serve with the vegetables, horseradish sauce and broth if using.
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