Step 1

Slice the cucumber crosswise as thinly as possibly, ideally with a mandoline. Place the slices in a colander, sprinkle them lightly with salt and toss gently to distribute the salt. Let the cucumber slices sit for 15 minutes (to draw out the moisture and bring out their flavor). Transfer them to paper towels and pat them dry.

Step 2

Lay out 4 slices of the bread. Spread one side of each slice with a thin, even coat of butter from crust to crust. Arrange the cucumber slices on each buttered slice, overlapping in 2 or 3 layers, to taste. (You might not use all the slices.)

Step 3

Butter one side of the remaining 4 slices of bread with a thin, even coat from crust to crust. Place them buttered side down over the layered cucumber slices to make 4 sandwiches.

Step 4

Gently hold the bread in place with one hand and use a serrated knife to trim off the crusts. Cut each sandwich into three equal rectangles. Arrange them neatly on a platter; serve right away.