The Caerphilly sandwich is defined by a crumble rather than a slice. Caerphilly is a Welsh territorial cheese, white, close, and notably crumbly, with a clean, mild, slightly sour and lactic edge and a hint of salt from its making. It does not behave like Cheddar between bread. Pressed against a slab and it fractures rather than folding, so the sandwich is built around a cheese that wants to break into a layer of moist, salty, faintly tart crumbs rather than sit as a continuous sheet. That texture is the whole character, and the bread and the counterweight are chosen to work with a filling that is, by nature, loose.
The craft is containment and matching the counter to a delicate cheese. Caerphilly crumbled into a sandwich will shed out of the sides on the first bite unless butter spread to the edges gives the crumbs something to hold to, so the butter here is structural as much as it is the salt bridge between cheese and wheat. The counterweight has to be gentle: Caerphilly's flavour is mild and slightly sour, and an aggressive pickle or a sharp chutney that a mature Cheddar would shrug off will simply bury it, so a thin scrape of a soft pickle, or just good bread and butter, lets the lactic tang read. The bread is plain because the cheese is quiet, and a strong crust would win an argument the filling cannot afford to have.
The variations stay across the British cheese bench rather than leaving it. Caerphilly with a leaf of crisp lettuce keeps the lactic note and adds water-crisp contrast; Caerphilly against thin apple brings sweet acid to the slight sourness; the broader territorial shelf, Wensleydale, Cheshire, Lancashire, runs the same crumbly-cheese logic with a different regional accent each time. Each of those is its own balance and its own article rather than being crowded in here.