On toast is the British open-face sandwich, and it gives up the second slice on purpose. A single piece of bread is toasted firm enough to act as an edible plate, then topped with a hot or strongly savoury layer and eaten with a knife and fork or in the hand over a plate. The bread is no longer a wrapper holding a filling in; it is a base holding a topping up, and toasting it is what stops it collapsing under the load.
The craft is keeping that base from going soft before the meal is over. The toast is taken further than for a sandwich, firm and dry, so it can carry sardines in oil, a wet pile of mushrooms, or melted spread without turning to mush. The savoury topping is intense and applied thin, because the format has no second slice to balance it and the whole effect rests on a strong flavour against plain, crisp bread.
The variations are a store-cupboard list. Sardines or mackerel on toast, the yeasty Marmite and beefy Bovril spreads on toast or in a sandwich, gentleman's-relish-style anchovy toast, garlic mushrooms, and the Welsh laverbread builds each keep the single-slice, strong-savoury logic. Each deserves its own article rather than being crowded in here.