Corned beef and cabbage is pretty much de rigeur for many Americans on March 17, whether they're of Irish descent or not. Oddly enough, it's not a common meal in Ireland, but that's not really the point, is it? The point is that corned beef and cabbage is delicious and completely seasonal. And if you have memories of your grandma serving it up to the whole family, all the better. Add some potatoes for bulk, if you like. (I like to boil small red potatoes in the broth left after cooking the corned beef - the broth is salty and flavorful and gives the potatoes great flavor - and serve them with a sprinkle of chopped parsley for some fresh green color on the plate.)
If you want to go all out, cure your own brisket to make the corned beef to cook (see How to Make Corned Beef for details), but most people will probably choose to buy a corned beef that has already been cured.
Put the corned beef in a large pot and cover it with water. You can leave it at that, but I like to add 2 Tbsp. of Pickling Spice or at least 1 Tbsp. of black peppercorns, as well as a quartered onion, a few carrots, and several celery stalks to add flavor to the broth. Bring all this to a boil, cover the pot, reduce the heat to keep a steady simmer going, and cook until the corned beef is super tender (when you pierce it with a fork, the fork should go in easily), 3 to 4 hours depending on how thick the corned beef is.
Trim a head of green cabbage and cut it into wedges, cutting so that a sliver of the central core holds each wedge together. Many people add the cabbage to the pot with the corned beef when the meat has about an hour left to cook, and this works fine. I prefer, however, to wait until the meat is done cooking, remove it from the pot, and cook the cabbage in the broth on its own (or with small red potatoes!) so I can cook it more precisely until it's perfectly tender but retains its full flavor and some texture, about 20 minutes.
Serve the corned beef, sliced across the grain, with the cabbage and plenty of mustard (I like grainy mustard with this) on the side for people to add.
Note: Want to use a slow cooker or an oven? See How to Cook Corned Beef for some options.