The Benedictine sandwich is a Louisville tea sandwich, and the thing that defines it is a spread, not a filling: Benedictine, a pale green cucumber and cream cheese paste with a precise set of problems already solved inside it. Cucumber is mostly water, and water is the enemy of a tea sandwich, which has to sit cut and plated without weeping into the bread. The spread is engineered around that single threat. Getting the cucumber into a cream cheese base without the sandwich turning to mush is the entire craft, and everything else is a soft slice of bread getting out of the way.
The craft is in the preparation of the spread before any sandwich exists. Cucumber is grated or pureed, then its liquid is pressed or wrung out hard, because any water left behind will migrate into the bread within the hour. The drained cucumber, along with a little grated onion, is folded into softened cream cheese stiff enough to hold a clean edge; a touch of salt draws out still more moisture, and a few drops of green coloring give the spread its characteristic pale tint. The bread is soft white sandwich bread with the crusts cut off, sliced thin, because a tea sandwich is judged on delicacy and a crust with chew breaks the form. The spread goes on edge to edge so the bread is sealed against what little moisture remains, and the sandwich is cut into fingers or triangles and served cool. This is finger food built for a tray and a crowd, made ahead and held, which is exactly why the moisture discipline in the spread matters so much: a Benedictine that weeps is a failed Benedictine.
The variations are mostly about what shares the bread with the spread. A version layered with thin-sliced cucumber adds crunch the paste alone lacks; one with bacon turns it savory and substantial; the spread itself is also used as a dip and a canape base entirely outside the sandwich. Those belong to the broader regional American specialty shelf rather than crowded in here, each with its own use and its own article.