Roast beef and onion answers a rich meat with bite rather than heat. The constant is cold rare roast beef, sliced thin, on good bread; what defines this version is onion, and the onion is doing a different job from the horseradish or mustard it replaces. A condiment supplies a sharp chemical heat that acts on the tongue; an onion supplies a pungent crunch and a sweet-sharp bite that lives in the structure of the sandwich itself. The defining fact is that the cutting note here has texture. Cold beef between bread is uniformly soft and dense, and a raw or pickled onion breaks that with a brittle, juicy snap as much as with flavour.
The craft is the onion's form, because raw onion is the most variable thing in the build. Sliced thick it is harsh and overpowering and dominates the beef entirely; sliced thin and across the bulb it reads as a sharp, manageable crunch that lifts the meat rather than fighting it. A milder red onion or a brief soak in cold water or vinegar takes the aggressive edge off without losing the bite, which is the calibration the whole sandwich turns on. The beef underneath follows the same rule as every roast sandwich: sliced thin and against the grain so a cold cut stays tender, and a marbled cut staying succulent where a lean one dries. Onion adds no fat, so butter on the bread does the lubricating a creamed sauce would have supplied, and it also seals the crumb against onion juice. A sturdy bloomer or white holds the filling without going soft under a wet, crunchy layer.
The variations split on how the onion is treated. Raw and thin is the sharp default; pickled brings vinegar and a firmer crunch; fried or caramelised swaps the bite entirely for a soft, sweet, mellow note, which is a genuinely different sandwich rather than a setting of this one. Past the onion, horseradish or mustard answers the beef with heat instead of crunch, watercress with a peppery leaf, Stilton with salt. Each deserves its own article rather than being crowded in here.