Bread and dripping is a two-ingredient sandwich in which one of the ingredients is usually thrown away. Dripping is the fat that runs off a joint of beef as it roasts, caught and left to cool until it sets firm and pale, carrying the savoury, faintly roasted taste of the meat it came from. Spread on bread, with no slice of meat at all, it stands in for the roast rather than accompanying it. That substitution is the whole sandwich and its entire reason for existing: a way to get the flavour of a beef joint from the part of the joint that would otherwise go in the bin. The bread is not a vehicle for a filling here; it is half of a pairing in which the other half is rendered fat.
The craft is temperature and what you reach down to include. Dripping is brittle straight from the cold and slick when warm, so it spreads cleanest at cool room temperature, going onto the bread like a firm butter and staying put rather than soaking through or sliding off. The valuable layer is the dark jelly that settles beneath the white fat as it sets, the concentrated meat juices and gravy that separated out, and a sandwich that digs down to take some of that jelly with the fat carries far more roast flavour than the pale top alone. The bread is chosen for structure, a sturdy white or a thick-cut loaf, because a dense, rich spread wants a crumb that holds it rather than collapses under it, and a firm grind of salt over the top sharpens a filling that is otherwise all depth and no edge. It is not toasted, because the point is set fat against soft bread, not a crisp base.
The variations are few and stay honest to the rendered-fat idea. Salt and pepper is the standard finish and often the only one. A deliberate scrape of the brown jelly worked through the fat is the richer build and the one most worth seeking out. Cold scraps of the beef itself folded in tip it over into a leftover-roast sandwich rather than a dripping one. Each deserves its own article rather than being crowded in here.