Cucumber and mint is the cucumber finger sharpened with one bright, sweet herb. On its own cucumber gives coolness and water and not much edge; mint supplies the lift it lacks, a clean, faintly sweet, slightly cooling note that amplifies cucumber's freshness instead of masking it. The mint is usually carried in the butter or worked through a soft spread, with thin cucumber laid over, so the herb sits against every slice. The single added note is the whole identity here. Take the mint away and it is a plain cucumber sandwich; the herb is the one thing that makes it its own pairing, and the build exists to let that brightness come through cleanly.
The craft is moisture control and placing the herb so it carries. Cucumber is sliced thin, salted, and drained before it meets bread, because an unmanaged slice weeps and softens the crumb and no amount of mint rescues a wet sandwich. The mint is shredded fine and folded into the butter or soft cheese rather than laid in whole leaves, for two reasons: a chiffonade distributes the flavour into every bite, and worked into the spread it sticks where loose leaves would slide off with the cucumber and bruise to a dark smear. The spread also seals the bread against the cucumber's water and grips the slices so the filling does not shear out the side. The bread is soft white, crustless, and deliberately plain, since the point of the sandwich is a quiet, bright pairing that an assertive loaf would bury, and it is assembled close to the table so the mint stays lively and the cucumber stays crisp.
The variations are the neighbouring herbs and richer bodies cucumber accepts. Dill swaps the sweet lift for a grassier, aniseed one; cream cheese gives the mint a fuller base to sit in; yoghurt worked into the spread pushes it toward a cooling, tzatziki-leaning note. Each is a distinct pairing of its own and deserves its own article rather than being crowded in here.