The Sunday roast sandwich is not a sandwich that gets made so much as one that gets assembled the next day from what the roast left behind, and that origin is its whole logic. Where the roast-beef sandwich isolates one meat and one condiment, this one folds the entire dinner into bread: cold sliced beef or whatever the joint was, stuffing, a Yorkshire pudding, cold roast potatoes, the congealed gravy, a stripe of horseradish or mustard. The defining fact is that it is a cold-next-day sandwich by design. A roast dinner is engineered to be eaten hot off the plate; this build accepts that the same components a day on, fridge-cold and set, are a different and in their own way better thing, and the sandwich is the format that makes that second life work.
The craft is managing components that have all changed overnight. Cold beef is sliced thin and against the grain because a roast cut thick and cold goes to rope between bread. The gravy has set to a savoury jelly out of the fridge, which is the asset the whole sandwich turns on: spread as a firm layer rather than poured, it supplies the moisture and seasoning the plate got from hot gravy without soaking the bread the way warm gravy would, so the build stays structural instead of collapsing. Stuffing brings its own seasoned bulk and a soft crumb; a split cold Yorkshire pudding can act as an internal layer or a wrapper. The bread has to have real structure, a bloomer or a sturdy white, to hold a heavy, mixed, slightly damp load, and butter or a smear of horseradish lines it so the slice is sealed before the jellied gravy goes near it. Everything depends on the leftovers having been good and on the cold setting them, not ruining them.
The variations are which Sunday it descends from rather than departures from the leftover logic. A beef roast carries horseradish and the set beef gravy; pork brings crackling and apple; lamb brings mint; the Christmas version runs turkey, stuffing, and cranberry through the same next-day frame. The Yorkshire-pudding wrap turns the pudding from a layer into the bread entirely. Each deserves its own article rather than being crowded in here.