Trim and thinly slice the cucumber (about ⅛ inch thick) using a mandoline or sharp knife. Sprinkle with ½ tsp salt and let rest in a fine-mesh strainer for 30–60 minutes, tossing occasionally. Pat dry with paper towels.
In a medium bowl, combine softened cream cheese, minced dill, chives, mayonnaise, remaining ½ tsp salt, and pepper. Stir until smooth and evenly mixed.
Spread about 1 ½ tbsp of herby cream cheese evenly over one slice of bread, leaving a small border. Arrange cucumber slices in overlapping rows. Top with a second slice of bread.
Using a serrated knife, trim off crusts and cut each sandwich into halves, quarters, or triangles. Chill for 10–15 minutes before serving.
