The Sandwich Œuf Dur is the plainest of the French egg sandwiches, and its plainness is the whole design. Œuf dur is the hard-boiled egg, cooked through, peeled, and sliced into rounds rather than mashed or bound with anything. The build is a length of bread, a film of butter or a thin swipe of mayonnaise on the crumb, the egg laid in overlapping discs, a turn of salt and black pepper, often a leaf or two of crisp lettuce. Nothing is whipped, nothing is folded; the egg keeps its shape, and the sandwich is a stack of plain components rather than a spread. That structural honesty is what separates it from its bound cousins.
The logic is the logic of a sliced solid behaving as the whole filling. Because the egg holds its form, it gives the sandwich a regular layered structure: discs shingled across the crumb sit flat and even, so every bite carries the same ratio of white to yolk. The cooked yolk is dry, which sets the constraint: without a fat carrier the sandwich reads chalky, so the butter or the thin mayonnaise underneath is doing real work, bridging the dry yolk to the bread rather than decorating it. Salt is not optional here, because a plain egg is mild and a sandwich without seasoning tastes of very little. The bread wants a soft crumb and a modest crust, since a hard crust fights the tender egg and tears the neat shingled layers apart on the first bite. A leaf of lettuce earns its place by adding the snap the soft filling lacks.
Variations are mostly a matter of what the egg is bound with, and each codified swap earns its own name. Fold the egg with mayonnaise into a salad and you have moved to the Œuf-Mayonnaise register; sieve the cooked yolk and pile it back over the white and you are making an Œuf-Mimosa; each is a different treatment of the same egg, and each gets its own entry rather than being crowded in here. Within the sliced-egg version the turns stay small: a few rounds of tomato, a layer of cress, a swipe of mustard worked into the butter. The Sandwich Œuf Dur belongs with the plant-forward and meatless builds the catalog groups under Sandwich Végétarien. Its specific contribution is the egg left whole and sliced, so the sandwich is an honest stack rather than a bound paste, and the cook's only real job is to season it and give the dry yolk a fat to lean on.