Roast beef and horseradish, in this reading, is the version made at home from the raw root rather than the jar. The constant is the same as its sibling: cold rare roast beef, thinly sliced, on good bread. What sets this one apart is the horseradish in its most uncompromising form, grated fresh from the root and used either neat or barely loosened, so the heat arrives sharp and volatile rather than rounded into cream. The defining fact is how quickly that heat lives and dies. Freshly grated horseradish releases its pungency on contact with air and loses it within the hour, which makes this a sandwich that is best built and eaten close together, and a different proposition from the deli-counter version built with creamed horseradish from a jar, which carries its own separate treatment.
The craft is timing and the cut, and the timing is the harder half. The root is grated at the last moment, because horseradish prepared and left to stand goes flat and bitter, and the whole reason to use it fresh is the brief fierce top note a jar cannot hold. Used neat it has no cream to soften it or to lubricate the bread, so the beef has to carry its own moisture: a marbled sirloin or rib sliced thin and against the grain stays succulent cold and tolerates the dry heat, where a lean topside turns to rope and leaves the sandwich harsh. A thin smear is the whole dose, because raw horseradish at full strength will overwhelm the beef entirely and reduce a good roast to a delivery system for sinus clearance. Butter on the bread does the lubricating the absent cream would have done, and a sturdy bloomer or white holds the filling without going limp.
The variations split first on exactly this point, fresh root against the creamed, cream-bound preparation, and the creamed build is its own sandwich rather than a milder setting of this one. Past that, the heat can be traded for English mustard, the bite for raw or pickled onion, the sharpness for peppery watercress, and the salt for crumbled Stilton. Each deserves its own article rather than being crowded in here.