Place the corned beef and the contents of the seasoning packet in a large Dutch oven or stockpot. Add the bay leaves and peppercorns. Cover with water, place the lid on the pot, and bring to a boil. Once it starts to boil, reduce the heat and simmer for 2 hours. Add the onions, carrots, and potatoes and continue to simmer for another 30 minutes or until the potatoes are tender. Using a slotted spoon, remove the potatoes and place in a mixing bowl. Add the cabbage to the pot and continue to simmer for another 15 minutes or until the cabbage is tender.
Add the melted butter, parsley, and a large pinch of salt and pepper to the potatoes. Toss to coat and keep warm while the cabbage cooks.
Remove the brisket and vegetables from the pot, slice the corned beef against the grain, and serve with the potatoes and vegetables.