The tongue sandwich is a deli sandwich whose defining quality is a texture no other cured meat on the counter has. Beef tongue is a single dense muscle with no grain to slice against and almost no connective tissue, so once it is pickled, simmered, and peeled it goes uniformly tender in a way pastrami and corned beef never do. There is no chew, no fibrous pull, no edge. Sliced thin and stacked on rye with mustard, it is the smoothest meat the Jewish deli serves, and that smoothness, mild and faintly sweet rather than peppery, is the whole reason it earns its own name on a counter built around spice and steam.
The craft is upstream of assembly, in the long cure and the cook. The tongue is brined like corned beef, then simmered for hours until it is fully soft, and the tough outer skin is peeled away while it is still hot, because it will not come off cleanly cold. What is left is sliced thin and stacked warm or cool depending on the house. The rye is the standard deli choice for the same reason it carries pastrami: a seeded, slightly sour loaf with enough body to stand up to a fatty meat without adding bulk, and the rye-to-meat ratio is kept deliberately lopsided so the bread gives the hand a grip and the mustard a home without competing. Mustard is the near-universal accent and it is doing real work here, because tongue is rich and gentle rather than sharp, and a hot, acidic mustard is the bite the meat itself does not provide. The build is otherwise plain on purpose: this is a sandwich that trusts a single well-cured muscle to carry it.
The variations are mostly the same impulse that runs the rest of the deli counter, a single swap earning a new ticket. Tongue is a frequent partner in combination sandwiches, stacked with pastrami or corned beef so the smooth meat plays against a peppery one in the same build. It shares its rye, its mustard, and its lopsided ratio with the brisket, chopped liver, and the smoked-and-steamed beef shelf it sits beside. Each of those is its own discipline with its own rules and deserves its own article rather than being crowded in here.