Corned beef is beef, usually brisket, that has been cured in a salt brine, usually with spices before it is cooked. "Corned" comes from the English term "Corn" meaning any small particle such as the coarse grained salt used for curing. "To Corn" means to preserve in a salty brine. Nitrates (saltpeter) are often added, as a preservative and to maintain a bright red color. "Corning" takes a week to three weeks to do so you might want to just buy an already corned beef and then slow cook it rather than trying to "corn' the beef yourself. However, "Cook's Illustrated" has a good corning recipe if you want to undertake it.
Mary Willis: If I cut a recipe in half, do I need to reduce the cooking time?
What matters most is the thickness of what you are cooking so let's say, you making a chicken recipe and you decide to cut it in half, as long as the chicken pieces are the same size and you have not cut them in half, the recipe will take the same amount of time.