The Isle of Mull Cheddar sandwich is a cheese sandwich whose entire identity is one specific farmhouse cheese, and the locality is not flavour copy, it is the sandwich. Mull Cheddar is made on a single Hebridean farm whose cattle are fed in part on the spent grain from a nearby whisky distillery, and the cheese that results is paler and looser than block Cheddar, sharp and almost savoury-bitter at the finish, with a tang that does not taste like the orange supermarket bar at all. Put any other Cheddar between the same two slices of bread and it is a different sandwich. The whole point of naming this one for a place is that the place is doing something to the cheese that travels into the bite, and the build exists to carry that and get out of its way.
The craft is restraint, because a cheese this assertive does not want help. Mull Cheddar is crumbly rather than rubbery, so it is broken or cut thick rather than thinly shaved, and it is not buried under a sweet pickle that would argue with a flavour already loud and slightly bitter on its own. Butter goes underneath to bridge the cheese's salt to the bread and to seal the crumb, but the counter, if any, is small and dry: a few oat biscuit crumbs, a thin scrape of chutney, a slice of apple, nothing that masks. The bread is plain, often a sturdy brown or an oatcake-adjacent loaf, because the cheese is the entire statement and an assertive bread would only fight a filling that needs no argument.
The variations stay on the regional cheese shelf and swap one strong farmhouse cheese for another. Orkney Cheddar brings a different island tang; a West Country mature carries its own crystalline crumble; the same cheese set against pickle and bread on a plate becomes a ploughman's rather than a sandwich. Each deserves its own article rather than being crowded in here.