Peel the cucumber and slice it into rounds about 1/8 inch thick with a sharp knife or mandoline.

Lay the rounds on a double layer of paper towel, sprinkle with 1/2 teaspoon salt, and let them sit for 15 minutes until they look glossy and slightly limp.

Pat the cucumber dry with fresh paper towel to remove the water that beaded on top.

Beat the cream cheese, butter, dill, white pepper and the remaining 1/2 teaspoon salt together until smooth and completely lump-free.

Spread the mixture edge to edge on all 16 slices of bread, so every bite gets some.

Layer the dried cucumber over 8 of the slices, overlapping the rounds slightly so there are no gaps.

Top each with a second slice, cream cheese side down, and press gently so the sandwich holds together.

Trim the crusts off with a long serrated knife, wiping the blade between cuts for a clean edge.

Cut each sandwich into 3 even fingers, arrange on a platter, cover with a lightly dampened paper towel, and refrigerate for 30 minutes before serving.