The West Country Farmhouse Cheddar sandwich is defined by a specific, protected style of cheese, not by Cheddar in general. This is the cloth-bound, traditionally made Cheddar from Somerset, Devon, Dorset, and Cornwall, matured slowly so it develops a dense, slightly crystalline body, a deep savoury depth, and a long sharpness that builds rather than hits and fades. The defining fact of the sandwich is the locality and the quality of that one ingredient. A generic block Cheddar in the same build is a different, flatter sandwich; the cloth-bound farmhouse version has a complexity that the rest of the sandwich exists only to frame.
The craft is the cut and the bridge. A properly matured West Country Cheddar is firm with a faint crumble at the edge of the slice, so it is cut thick enough to give that crystalline texture room in the mouth without drying it out, never grated, because grating throws away the body that is the whole reason to use this cheese. Butter is spread to the edges as a structural layer, carrying the cheese's salt evenly across the crumb and stopping the bite arriving as bread then cheese then bread. The bread is deliberately plain, a good soft white or a plain wholemeal, because a cheese with this much depth needs no help and an assertive loaf or a heavy condiment would only mask what you went to the trouble of buying.
The variations are restrained on purpose, because the cheese is the event. A sharp pickle or a fruit chutney sets an acid counter against the savoury depth; a slice of crisp apple does the same with less sweetness; a ploughman's stands the same wedge against pickle and bread on a plate rather than between slices. Each deserves its own article rather than being crowded in here.