I love carrots so I vote yes. Also vote yes to parsnips.
As you point out, corned beef and cabbage is Irish-American rather than Irish (as is the secular celebration of St. Patrick’s Day). That makes it unlikely that it represents the colors of the flag, which wasn’t recognized as being a national flag until 1916. Corned beef and cabbage seems to have been adopted by the Irish in the US by at least the 1860s.
All I know is that my mother, whose maiden name was Rosie O’Rourke and whose grandparents came from Ireland, never put carrots in our corned beef and cabbage.
Mrs. L.A. doesn’t really care, but she voted for carrots.
Yes, carrots.
But braise the cabbage, don’t boil it.
Which is the only vote that counts.
Not a big fan of boiled carrots but others in my family like them so in they go and I just avoid them.
But where’s the onion? You have to throw some onions in the mix to give it the proper flavor.
I used to. I decided CB&C doesn’t need onions.
This is the way I do it. Simple and tasty.
You need the onions to make hash. In fact you need everything to make a good hash. Then you can plop a fried egg on top and have one of the best breakfasts on the planet.
I’ve mentioned this before but not for a while and this seems like the thread.
Use the skimmed corned beef broth to make the best split pea soup you’ve ever had.
A few of those carrots and a some shreds of corned beef can go in the soup, too.
I simmered a 3lb point on Sunday to eat this week.
It came out great and was only $6 and change.
This time of year, I go a little crazy with the buying of so much loss-leader corned beef.
The cheaper brand is $1.99/lb points, $2.49 flats.
The premium Vienna and Harrington’s were around $5.50/lb, I bought a few.
It freezes well and I like to have it on hand.
When it gets a little nicer out, I’ll slather one in yellow mustard and the rub black pepper and ground coriander all over.
Smoke overnight for some fantastic pastrami.
Except leftover corned beef does not get eaten as hash. It gets eaten with leftover cabbage. When the cabbage runs out, it goes on rye, with some mustard and Swiss cheese.
I made split pea soup with the broth once.
Once.
It was entirely too salty.
You should taste the broth first and water it down (or use some other sodium-free or low sodium liquid) to a salt level you like. The salinity of the broth you get from corned beef depends on a few factors, so you really should check for that first.
And, yes, it makes for a lovely split pea or any kind of bean soup.
This and the potato remarks makes me think that you and I use very different amounts of water.
It sounds like you’re barely covering it while mine is under five inches of water.
I baked corned beef in the oven once. Once. Without a bunch of water, the salt has no where to go except back into the ever shrinking meat. This remains a problem when I smoke CB briskets. I soak the meat in water that I change about every 8-12 hours over the course of a few days. Even then, it sometimes comes out a bit too salty.
Yes to carrots. Corned beef (preferably point cut), cabbage, carrots, small red potatoes, and a secret blend of spices, in a great big boiling pot.
The flat cut is usually less fatty.
“Corned” beef is salted beef brisket. If anyone is looking for less salt, just buy brisket, and salt to taste.
Well, kind of. It’s (usually) wet cured brisket, usually with a bit of nitrite/nitrate in it (which gives it that rosy red color and helps contribute to the “cured” taste.) Just salting brisket gives you salted brisket (unless you do it for about a week–then you’ll have dry cured corned beef.) And don’t forget all the pickling spices.
If you want that corned beef flavor with less salt, soak your corned beef with a few changes of water, as suggested above.
About the carrot, I plan to put some in our corned beef and cabbage this weekend. I never ate it or cooked it until marrying into an Irish American family, and I cook it the way my MIL used to, with potato, carrot, parsnip, turnip and onion.
I’ve heard this statement a number of times and have friends from Limerick who back it up. However I’ve seen references to corned beef and cabbage as an ordinary dish in Irish books from 100 years ago. Is it possible that in Ireland it’s a forgotten dish, but it survived in the Irish-American community?
This is from James Joyce’s Dubliners, the story “A Painful Case”, published in 1914 but written before 1905. This short story collection is “a naturalistic depiction of Irish middle class life in and around Dublin in the early years of the 20th century.”
“He dined in an eating-house in George’s Street . . . where there was a certain plain honesty in the bill of fare . . . . every evening [he] walked home from the city after having dined moderately in George’s Street and read the evening paper for dessert.
One evening as he was about to put a morsel of corned beef and cabbage into his mouth his hand stopped. His eyes fixed themselves on a paragraph in the evening paper which he had propped against the water-carafe. He replaced the morsel of food on his plate and read the paragraph attentively. Then he drank a glass of water, pushed his plate to one side, doubled the paper down before him between his elbows and read the paragraph over and over again. The cabbage began to deposit a cold white grease on his plate.”
https://www.gutenberg.org/files/2814/2814-h/2814-h.htm
It’s also mentioned in Joyce’s Ulysses, set in 1904 and written 1914-17, where at “the Burton restaurant”, which sounds like a dive, with people “swilling, wolfing gobfuls of sloppy food”, someone orders “One corned and cabbage”
http://www.gutenberg.org/files/4300/4300-h/4300-h.htm
I cook the meat and potatoes (and carrots, when I use them) in a 6-quart slow cooker, and it’s usually about a three-pound cut of meat. So yeah, there’s just enough water to cover everything – as long as it’s not higher than the rim of the crockery insert.
Yes, you are correct. Salted is salted, and brined is soaked in salt water.
Decades ago, my FIL was told to “lay off the salt” and we would make (un)corned beef (aka brisket) and cabbage with red potatoes, and carrots, plus the same blend of spices we use for real corned beef. I thought it suffered from a definite lack of salt. Still good but…
Brisket is delicious in all its forms! Your dad basically made a pot roast. You weren’t missing just the salt, though. You were missing the cured flavor that a week to a month of soaking in cure will do. 
If for no other reason, add carrots just for the color alone. It would look boring if you excluded them. I like my food colorful!!