In a large pot over medium heat, combine all the brine ingredients except the ice cubes. Stir well to dissolve the sweetener. Bring the ingredients to a boil, then remove from the heat and let cool.

Place the brisket in a large freezer-safe bag or glass container. Add the ice cubes to the brine. When the brine is cold, pour it into the bag with the brisket, making sure that the meat is completely submerged. Set the brisket in the refrigerator to brine for at least 3 days or up to 5 days.

When you are ready to cook the brisket, discard the brine. Rinse the brisket under cold water and place it in a large pot. Add the garlic, pepper, and water. Simmer, covered, for 3 to 4 hours, until the meat is fork-tender, adding water as needed so that the brisket does not dry out.

If desired, add the chopped cabbage during the last hour of cooking. Leftover corned beef can be refrigerated for up to 4 days or frozen for up to 3 months.