We ended up eating the corned beef on Sunday and fininsh the leftover meat in sandwiches on Monday and Tuesday. But that didn't stop me from making the hash with the remaining vegetables.
Drain the leftover cabbage, potatoes, etc., well. Saute a green pepper in a pan with some butter. Add the vegetables and cook a little to get rid of most of the remaining liquid. Spread the vegetables evenly.
Take a lid from a smaller pan and push down hard on the mix. Leave the lid on and cook for about ten minutes. Remove the lid, stir the vegetables, and repeat the process.
The mix turned out great! The vegetables carmalized up nicely (remember rule #2).