The Omaha reading of the Reuben is the home-team version of a sandwich the rest of the country thinks of as a New York deli object. Omaha makes a competing claim on its invention, and whether or not the claim holds, the result is that the Reuben in Omaha is treated as a local sandwich rather than an import: it is a steakhouse and supper-club fixture in a beef town, plated next to the strip and the prime rib rather than pulled hot from a deli case under a mountain of pastrami. That context changes how it is built. In a city organized around its beef, the corned beef is the point and the build is steakhouse-tidy, a clean, square, knife-and-fork sandwich rather than the deli's overstuffed argument.
The craft is the same four-component system every Reuben runs, executed with restraint. Corned beef, brined and boiled lean and sliced against the grain, is portioned to the rye rather than piled past it, so the sandwich holds its shape under the spatula. Sauerkraut is wrung out hard before it goes in, because the failure mode is water flooding the bread and the bottom slice giving way. The Swiss is laid against the rye on both inner faces with the kraut and meat sealed between, so the melting cheese glues the structure and shields the bread from the wet kraut at once, and the Russian or Thousand Island dressing works from inside the sealed sandwich rather than running out of it. The seeded rye is griddled in butter on patient heat until it reaches deep gold at the exact moment the Swiss is fully molten. In a steakhouse kitchen that griddle discipline is the whole job: the sandwich arrives crisp, square, and cut clean, eaten with a fork as readily as the hand.
The variations are the same tightly bounded set the Reuben always spawns: the Rachel swapping coleslaw for the kraut and often turkey for the corned beef, the pastrami substitution pushing it smokier, the pumpernickel version changing the loaf but not the logic. Each is a single substitution on a fixed technique, and each deserves its own article rather than being crowded in here.