The Cheshire sandwich is built on a cheese that crumbles rather than slices, and the crumble is the defining fact. Cheshire is a pale, loose-textured, slightly saline territorial cheese with a clean acidity and a faint mineral edge, and it does not cut into clean slabs the way a firm Cheddar does. It breaks. Pressed into a sandwich it sits as a layer of moist, salty crumbs rather than a solid sheet, which means the bread, the butter, and the way the thing is assembled all have to account for a filling that will not hold itself in one piece.
The craft is managing that crumble while letting the cheese's quiet salinity carry the sandwich. Because Cheshire is friable, it is crumbled deliberately and laid in an even bed rather than fought into slices that will only fall apart in the hand, and it is pressed lightly so the crumbs knit against the bread instead of spilling out of the sides at the first bite. Butter to the edges does double work here: it carries the cheese's gentle salt across the slice and, just as importantly, it tacks the loose crumbs to the crumb of the bread so the structure holds. The bread is soft and plain on purpose, because Cheshire is a restrained, slightly sour cheese with none of Cheddar's loud sharpness, and an assertive crust would simply bury it. The salinity is the seasoning; nothing else is needed, and a heavy hand with pickle would drown a cheese that speaks softly.
The variations are the rest of the British territorial bench, each a different decision about texture and salt. Crumbly Lancashire reads similarly but tangier; Wensleydale is milder and is set against something sweet; the blue-veined Cheshire pushes the saline edge much harder; a fruit chutney or a few celery leaves answer the cheese's dryness without shouting over it. Each deserves its own article rather than being crowded in here.