The Scottish Cheddar sandwich is a cheese sandwich whose identity is the particular cheese, not the build. This is not anonymous block Cheddar but the firm, close-textured cheese made in Scotland, the island and creamery Cheddars of Orkney, Mull, and the Highlands among them, sharper and more mineral than soft mass-market versions, with a tang that comes from the milk and the cold. The sandwich is that cheese cut thick on plain bread with butter underneath and one acid counter, and the defining fact is that the cheese is both the structure and the flavour. There is almost nothing else in the build to carry it, which is the point: a Scottish Cheddar at its best is loud and specific enough that the sandwich can do nothing else and still be worth eating, and swapping in a bland Cheddar leaves a lesser sandwich with nothing to hide behind.
The craft is the cut and the bridge. A firm Cheddar like this wants to be sliced rather than grated and cut thick enough to have presence in the mouth without drying it, because a thin shaving disappears and a slab leaves the jaw working through chalk. The sharpness and the faint crystalline crumble of a mature Scottish Cheddar are the only seasoning the sandwich gets, so the cheese has to be good. Butter is structural here as much as flavour: spread to the edges it carries the cheese's salt evenly across the slice and waterproofs the crumb so a sharp pickle or chutney does not soak through and turn the base to paste. The bread is soft and plain on purpose, because a cheese this assertive needs no help and a strongly flavoured loaf would only argue with it.
The variations are the rest of Britain's regional cheese shelf met with the same plain frame. The Orkney, Isle of Mull, and West Country Cheddars push the sharpness and the sense of place in their own directions; mature and vintage versions take it further still. Cheese and pickle, cheese and onion, and the ploughman's that sets the wedge against bread and chutney rather than slicing it all keep the same logic, and a blue such as Stilton crumbled for distribution is the same idea with a different cheese. Each of those deserves its own article rather than being crowded in here.