Ah, the wonderful world of 2001 wherein Diomedes lives, where a Delmonico Steak costs $7.50 whereas the wonderful world of 2016 where I am writing from the Steak costs $13.89. Times have changed.
Named after the Delmonico Restaurant in New York City, there is some disagreement on what a Delmonico Steak actually is. This is due mainly from historical accident as the people who originally knew the cut have all died and didn’t bother to write it down. What we do know is that it was a marbled, high quality piece of meat originating in the 1800s Delmonico Restaurant. The current Delmonico Restaurant sells the Steak as two heart cuts of a Ribeye. This is a rare way to prepare a Ribeye because it ruins the rest of the Ribeye making it unsellable except as grinds.
Some people argue the Delmonico is actually a very well-marbled boneless Top Sirloin (that’d be a Rump cut for you British noders out there) or a New York Strip Steak. Others say it is cut from the chuck eye, but can only be the steak cut right before the Ribeye. Then some say the Delmonico is any bone-in Ribeye. What a Delmonico is depends largely on where you are buying them from, though everybody agrees they are high-quality, very fatty steaks.
My work sells Delmonicos as a boneless Ribeye but cut from the large end of the Prime Rib Roast making it significantly fatter than a regular Ribeye. The Delmonico can be identified from a regular Ribeye by the square of fat in the middle-ish top right of the steak and the marbling spreading out from that point.
Delmonicos do best on the grill, but tastes great cooked in any number of ways. Because of the high fat content it is guaranteed to taste good as long as you don’t do something insane to it, like boil it or some other kind of blaspheme.
Also known in various quarters as a Boneless Club Steak, Kansas City Strip Steak, or Shell Steak.
Update: 2017; 14.89.