36 dime-thin slices of hothouse or small Kirby cucumbers, or as needed
3 Tablespoons unsalted butter, at room temperature
1 Tablespoon finely chopped fresh dill
8 Slices of bread, such as a good high-quality thin sliced bread, Pepperidge Farm makes both a wheat and a white version, these are very thin loaves and are perfect for finger sandwiches
Spread the cucumber slices out in a single layer on a sheet of paper towel. Sprinkle lightly with salt and let stand.
Beat the butter and dill together in a small bowl. Spread the butter onto one side of 8 slices of bread. There will be enough butter to coat each one lightly.
Arrange the cucumber slices overlapping very slightly over 4 of the bread slices. Top with the remaining bread, pressing each gently. Cut off the crusts and cut each sandwich into 4 squares or triangles.