Heat a large 12 inch skillet over medium high heat for at least 2 minutes. Open your package of corned beef and drain the brine into the sink. There is no need to rinse the corned beef. Some corned beef brands include a packet of spices*, but sometimes the spices are mixed into the brine. Save the spice packet if there is one.
Add 2 tablespoons oil to the hot skillet; it should shimmer immediately. Swirl to coat, then add the drained corned beef. Sear for 2-4 minutes on one side until golden brown, then carefully flip with tongs and sear the other side for another 2-3 minutes.
Place the seared corned beef in your crock pot, fat side up, but don't put the skillet in the sink yet.
In a glass measuring cup, combine 1 and 1/2 cups beef broth with 3 tablespoons whole grain mustard. (I always use Better Than Bouillon Beef Base and water to make my broth.)
Add the liquid to the pan that you seared the beef in, and turn the heat to medium high. Let the mixture bubble as you scrape up the browned bits. Pour the mixture over your corned beef into the crock pot.
Smash 6 cloves of garlic with the side of a chef's knife, peel, and add to the crock pot. Roughly slice an onion into wedges and add to the pot. Add about 15-20 whole peppercorns. Add 8-10 sprigs of fresh thyme and 2 bay leaves, tucking them into the liquid. Sprinkle the spice packet* over everything.
Cover with the lid and cook on low for about 6-7 hours.
Prepare your carrots. Peel them and slice each carrot into thirds, slicing any large segments in half lengthwise. I actually prefer the larger carrots myself, so don't break your back here.
Add the carrots on top of the beef, cover again and cook for another 1-2 hours.
Prepare the cabbage. Slice the cabbage in half, then cut out the stem. Slice the cabbage into large wedges. Melt 1/2 cup butter in a 12 inch skillet over medium high heat. Add all the cabbage (it looks like it won't fit, shove it all in!) and sprinkle with 1 teaspoon kosher salt. Saute, stirring occasionally for about 10 minutes, until the cabbage is slightly wilted but not quite to the point that you would snag a bite yet. Add the cabbage on top of the carrots, and continue cooking on low for another 30-60 minutes, until the cabbage is softened and has absorbed some of the corned beef flavor.
Meanwhile, make a batch of Roasted Red Potatoes in the oven. Potatoes do not belong in the crock pot. (Of course you can do it if you want. Add them with the carrots, they need 2-3 hours to cook. But don't blame me when you get smooshy mooshy gray potatoes.) To serve: I like to serve corned beef on a large platter. I think it looks best when the ingredients are presented separately. Use a slotted spoon to remove all the cabbage to a colander to drain slightly. Place all the carrots together on the platter. Add the drained cabbage to the platter next to the carrots. Remove the corned beef to a cutting board and let rest for about 10 minutes. Slice against the grain, then add to the platter. Leave all the broth, onions, garlic, thyme stems, and bay leaves behind. (You can eat the onions and garlic if you want, I find them to be so overcooked that they are unappetizing. We add them to help flavor the other ingredients.)Add the roasted potatoes to the platter. Garnish with chopped parsley and chopped chives. Serve with a batch of homemade Horseradish Sauce! It's super easy to whip up, and compliments the corned beef perfectly. Don't skip it!