1 3 lb. corned beef brisket (in package with spice packet)
2 large carrots, peeled and cut into ½ inch coins
1 medium yellow or sweet onion, thinly sliced
1 large garlic clove, thinly sliced * large bay leaf
1 12-ounce bottle of dark beer such as stout or porter (for a nonalcoholic version, replace the beer with an additional 1½ cups beef broth)
1 tbsp. apple cider vinegar * 1 tbsp. light brown sugar
1 tsp. Dijon mustard * 1 to 2 cups beef broth (additional as needed)
6-8 medium red potatoes, rinsed and quartered
1 small head green cabbage
Assemble the corned beef: Place the carrots, onion, garlic and bay leaf in the bottom of a 6-quart slow cooker.
Place the corned beef on top of the vegetables.
Whisk the spice packet that came with the corned beef together with the beer, vinegar, brown sugar and mustard. Pour over the corned beef, then pour in the 2 cups beef broth. The liquid should completely submerge the vegetables and partially cover the corned beef — the amount needed to do this will vary depending on the depth and model of slow cooker, so add more broth as necessary.
Place the potatoes on top of the corned beef.
Close the slow cooker and cook on low for 6½ hours before adding the cabbage. (If your slow cooker has a warm function, you can hold the beef and vegetables for up to 90 minutes before adding the cabbage if needed.)
Add the cabbage: Core the cabbage and slice into 8 wedges. Open the slow cooker and place the cabbage on top of the potatoes and corned beef. Close and cook for another 1½ hours, until the cabbage is tender but still retains its shape.
Finish and serve: Remove the cabbage with tongs and then carefully lift the corned beef out of the liquid and transfer to a cutting board. Strain the potatoes, carrots and onions from the cooking liquid, discarding the liquid. Slice the corned beef and serve with the cabbage and vegetables.