The Beef 'n Cheddar is defined by the fact that its cheese is a sauce and its sharpness is a dressing, not a vegetable. The sliced-roast-beef sandwich usually answers a wet, salty pile of meat with either jus and a hard pepper relish or a plain roll and mustard. This build keeps the thin-sliced beef and answers it with two liquids instead: a warm cheddar cheese sauce that pools into the meat, and Red Ranch, a sweet-tangy tomato-based dressing that supplies the acid a sandwich like this normally gets from a pickle or a giardiniera. The onion roll is the third decision, a faintly sweet, oniony bun chosen to stand against both the cheese sauce and the dressing rather than disappear under them.
The craft is in balancing two pourable elements on bread without flooding it. Roast beef is sliced thin so a warm pile stays tender rather than turning to rope, and it is held hot so the cheese sauce keeps its flow when it meets the meat. The cheddar sauce is a pourable emulsion rather than a melted slice, which means it coats every surface and binds the beef the way a draped slice never could, but it also brings moisture the bun has to survive. Red Ranch does the structural job that an acidic counter does in any rich beef sandwich: it cuts the fat of the cheese and the salt of the meat with sweetness and tang, and because it is a dressing rather than a relish it has to be applied so it seasons without soaking through. The onion roll earns its place by having enough crumb structure and its own sweet, savory flavor to read against the sauce instead of dissolving into it. The sandwich is built hot and eaten promptly, since both the cheese and the dressing work through the bread quickly.
The variations stay inside the sliced-beef-and-sauce logic. A double stacks more beef and forces the roll to carry more cheese and dressing. A plain reading drops the Red Ranch and lets the cheddar sauce and beef stand alone. The same thin-sliced roast beef on a toasted bun with a thin tangy sauce is its own simpler build. Each of those is its own preparation and deserves its own article rather than being crowded in here.