Step 1: Prepare the Pickle-Brined Cabbage (Optional, but Highly Recommended). In a small bowl or jar, combine the ½ cup of dill pickle brine and the ½ cup of water. Add 2-3 of the cabbage wedges to the brine, making sure they are submerged. Let them sit at room temperature for at least 30 minutes, or refrigerate for up to a few hours. This will give them a subtle pickle flavor.

Step 2: Combine Ingredients in Pot. In a large pot or Dutch oven, combine the corned beef brisket, the contents of the spice packet, 3 quarts of water, the quartered onion, carrot chunks, celery pieces, and salt.

Step 3: Bring to a Simmer. Bring the mixture to a simmer over medium-high heat, skimming off any foam that rises to the surface.

Step 4: Cover and Simmer. Once simmering, cover the pot, reduce the heat to low, and simmer until the meat is almost fork-tender, about 3 hours.

Step 5: Add Potatoes. After 3 hours, add the halved red potatoes to the pot. Continue to simmer, uncovered, until the potatoes are almost tender, about 30 minutes more.

Step 6: Add Cabbage. Place the remaining (non-brined) cabbage wedges on top of and around the meat. Cover the pot and simmer until the cabbage is tender, 20 to 30 minutes more. Add the drained, pickle-brined cabbage wedges during the last 10 minutes of cooking.

Step 7: Rest the Meat. Remove the corned beef from the pot and transfer it to a cutting board. Let it rest for 10 to 15 minutes before slicing. This allows the juices to redistribute, resulting in a more tender and flavorful meat.

Step 8: Slice and Serve. Cut the corned beef across the grain into thin slices. Serve in a bowl or on a platter, ladling the vegetables and broth over the top.

Step 9: Garnish and Enjoy! Garnish with pickled mustard seeds (if using) and serve with chilled dill pickle spears on the side.