Cheese and coleslaw is a deli-counter sandwich in which the coleslaw is not a side at all but the only seasoning the cheese gets. A plain Cheddar sandwich needs a counter, an acid or a sharp note to cut the fat, and here the slaw is doing that entire job by itself. It brings everything the cheese lacks in one spoonful: the tang of the mayonnaise dressing, the raw bite and sweetness of cabbage and carrot, and a cold crunch against the dense uniform cheese. There is no separate pickle, no mustard, no chutney. Take the slaw out and you have unseasoned Cheddar on bread, which is exactly why the slaw has to carry the whole flavour of the sandwich rather than merely sit in it.
The craft is making one component do several jobs without overwhelming the cheese. The slaw is seasoned and dressed to be assertive enough to register against a thick slab of Cheddar, sharp and savoury rather than bland and sweet, because a timid supermarket slaw disappears entirely behind the dairy and leaves the sandwich tasting of nothing in particular. It is bound tight rather than loose, partly so it does not slide and partly so the dressing's tang stays concentrated where the bite lands. The Cheddar is cut with real presence so it is a partner to the slaw rather than a wet vehicle for it. Butter to the edges seals the crumb and bridges the cheese's salt across the slice. A sturdy bread carries a heavy, dressed filling that soft white could not hold.
The seasoning-by-slaw idea has obvious relatives. A spiced or mustard-laced slaw pushes the counter harder; cheese with a separate pickle splits the job back into two components; ham alongside the slaw adds a second savoury layer. Each deserves its own article rather than being crowded in here.