This is not a traditional Irish dish, but we have made it one at our house.  Around  this time of year, the  corned beef brisket is plentiful and cheap, and the cabbage is only 7 cents a pound.

 
 
1 corned beef brisket, about 3-4 lb.
yellow mustard
brown sugar
1 medium head of cabbage, cut into chunks
4-5 potatoes, peeled and quartered
 
 
 
 
Put corned beef brisket in pot. Cover with water.
Bring to boil. Cover and simmer for 3 hours. Remove brisket. Save liquid.
Preheat oven to 350 degrees. Place brisket, fat side up, in  foil lined baking pan. Spread thin layer of mustard on top of brisket. Top this with brown sugar. Bake for 30 minutes.
Into the liquid, put the cabbage and potatoes. Cook over medium heat for 30 minutes.