Step 1: Rinse the corned beef brisket under cold water to remove any excess brining liquid. Place the brisket in a large Dutch oven or stockpot. Add the pickling spice packet that came with the corned beef, the quartered onion, smashed garlic, and apple cider vinegar (if using). Pour in enough water to completely cover the brisket.
Step 2: Bring the liquid to a boil over high heat, then reduce the heat to low, cover the pot, and simmer for 2.5 to 3 hours, or until the corned beef is fork-tender. The exact cooking time will depend on the size and thickness of your brisket. Check occasionally to ensure the liquid is still covering the meat; add more hot water if necessary.
Step 3: After 2.5 hours, add the potatoes and carrots to the pot. They should cook submerged in the flavorful broth alongside the corned beef. Continue to simmer, covered, for another 20-30 minutes, or until the vegetables are nearly tender.
Step 4: Gently place the cabbage wedges into the pot, nestling them around the corned beef and other vegetables. Ensure they are partially submerged in the liquid. Cover again and continue to cook for another 15-20 minutes, or until the cabbage is tender-crisp. You want the cabbage to be tender but not mushy.
Step 5: Carefully remove the corned beef from the pot and place it on a cutting board. Cover it loosely with foil and let it rest for 10-15 minutes. This resting period is crucial for allowing the juices to redistribute, ensuring a tender, moist slice.
Step 6: While the corned beef rests, remove the vegetables from the pot using a slotted spoon and arrange them on a large serving platter. Keep them warm. You can discard the onions and garlic from the broth, or serve them if desired.
Step 7: Slice the corned beef against the grain into 1/4-inch thick slices. Arranging the slices neatly on the platter with the vegetables. You can drizzle some of the cooking liquid over the meat and vegetables for extra moisture and flavor.
Step 8: Garnish with fresh chopped parsley, if desired. Serve immediately with coarse-grain mustard or horseradish on the side.