The egg salad sandwich is the lunch-counter test of how little a sandwich needs to be good: chopped hard-boiled egg, mayonnaise, salt, and soft sliced bread, with nothing to hide behind. Everything depends on the bind, because there are no other ingredients carrying the sandwich. Get the ratio of mayonnaise to egg wrong and it is either dry crumble or wet paste, and either way the failure is the whole sandwich. The restraint is the design, not an accident of poverty.
The craft is in the egg and the proportion. The eggs are boiled to a set but not chalky yolk, then chopped rather than mashed so the salad keeps some grain instead of going to spread. The bind is enough mayonnaise to hold the chop together and no more, seasoned with salt and usually a little mustard for sharpness against the fat, and given crunch and acid by finely diced celery, onion, or pickle so the texture is not uniformly soft. The bread is deliberately plain soft white or wheat, sliced thin, because a crust with real chew fights a filling that has none. It is spread to the edges, closed, and cut on the diagonal, and it is built to be eaten soon: the bind sits against the crumb and a sandwich left too long becomes one wet thing. Lettuce goes in as the cold, crisp counter when it goes in at all.
The variations are small and honest. A dusting of paprika and a fold of fresh dill is the classic dressed-up version; curry powder turns it into a different sandwich entirely; chopped pickle and a heavier hand with mustard pushes it sharp. The tea-sandwich form trims the crusts and cuts it into fingers for a different occasion. Each of those is its own balance and deserves its own article rather than being crowded in here.