The corned beef and cabbage I gew up eating always had potatoes and carrots, and sometimes turnips and parsnips.
Parsnips would be good…but "corned beef and cabbage" pretty much implies that’s all you put in the pot. At least, that’s what my Irish grandmother always said. [;)]
@ Big Ugly Mich:
Corned beef is salt cured for about a week (if done properly), whereas just plain beef brisket is not.