Place the potatoes, carrots, celery, onions, garlic, and thyme in a large slow cooker (6 quarts). Rinse the corned beef if the package directs. Then, either way, place the brisket on top of the vegetables and sprinkle over the pickling spices in the packet. Pour in the beer and add enough water to just cover the meat. Cover and cook on the high setting for 4 hours or the low setting for 8 hours.
Add the cabbage, cover and cook on the low setting for 1 more hour.
Meanwhile, in a small bowl, stir together the sour cream, horseradish, mustard, parsley and lemon juice. Season with salt and pepper.
Remove the meat and vegetables from the slow cooker and let the meat sit for 10 minutes before slicing across the grain. Serve with the vegetables and the Horseradish Cream Sauce. Spoon a bit of the cooking liquid over the corned beef and vegetables.
Notes
Tips for Making Corned Beef in the Slow Cooker
Unless the package directs, you do not need to rinse the corned beef before cooking it. Just add the seasoning mix in the little packet to the meat as directed in the recipe.
The liquid should just cover the meat, which will result in a consistently tender piece of corned beef.
Whatever temperature you choose to cook your corned beef in the slow cooker, you will add the cabbage to the slow cooker for only the last hour of cooking. This allows the cabbage to soften and become tender, but it also allows the cabbage to retain some texture and its pretty pale green color. Carrots, onion, and celery are the other vegetables in the mix, but I prefer to let those get nice and soft with the meat.
Slice the meat across the grain for it to be at its most tender.