Step 1: Trim the corned beef brisket of any excess visible fat. While some fat is desirable for flavor, too much can make the dish greasy. Use a sharp knife to carefully remove the thickest layers of fat, leaving a thin layer for flavor.

Step 2: Lightly spray the inside of a large (6-quart or larger) crockpot with nonstick cooking spray. This will help prevent the vegetables from sticking to the bottom of the pot.

Step 3: Arrange the sliced onion, halved or quartered red potatoes, and baby carrots in the bottom of the prepared crockpot. These vegetables will form a bed for the corned beef, preventing it from sticking and allowing it to cook evenly. Layering the vegetables on the bottom also ensures that they absorb the flavorful broth as it cooks.

Step 4: Place the corned beef brisket on top of the vegetables in the crockpot. Ensure the brisket is centered and nestled among the vegetables.

Step 5: In a separate bowl, whisk together the beef bouillon cube, minced garlic, Worcestershire sauce, dry mustard, and low-sodium beef broth until the bouillon cube is dissolved. This mixture will create a flavorful braising liquid for the corned beef and vegetables. The beef bouillon enhances the savory flavor of the broth, while the garlic, Worcestershire sauce, and dry mustard add depth and complexity.

Step 6: Pour the liquid mixture over the corned beef brisket, ensuring that it covers the meat and vegetables as much as possible. The liquid will help to keep the corned beef moist and tender as it cooks.

Step 7: If desired, sprinkle the spice packet that comes with the corned beef brisket over the top of the meat. These spice packets typically contain a blend of coriander, peppercorns, and other aromatics that complement the flavor of the corned beef. If you don't have a spice packet, you can substitute with a combination of ground coriander, black peppercorns, and a pinch of ground cloves.

Step 8: Cover the crockpot with the lid and cook on the low setting for 8-10 hours, or on the high setting for 4-5 hours. The cooking time will vary depending on the size and thickness of your brisket. Properly cooked corned beef should reach an internal temperature of at least 145°F.

Step 9: During the last hour of cooking, add the cabbage wedges and caraway seeds to the crockpot. Nestle the cabbage wedges among the corned beef and vegetables. The caraway seeds add a subtle, earthy flavor that complements the cabbage and corned beef.

Step 10: Continue cooking for the remaining hour, or until the cabbage is tender-crisp. Be careful not to overcook the cabbage, as it can become mushy. The cabbage should still have a slight bite to it.

Step 11: Once the corned beef is cooked through and the cabbage is tender, carefully remove the corned beef from the crockpot and place it on a cutting board. Let it rest for at least 10-15 minutes before slicing against the grain. This will help the juices redistribute, resulting in a more tender and flavorful cut of meat.

Step 12: Discard the cooking liquid from the crockpot. This liquid will be very salty, so it is not recommended for consumption.

Step 13: Slice the corned beef against the grain into thin slices. Serve the sliced corned beef with the cooked potatoes, carrots, and cabbage.