Place the cream cheese in a medium-sized mixing bowl and allow it to soften at room temperature for about 1 hour.
Meanwhile, slice the English cucumber crosswise into ultra-thin rounds, about 1/8-inch thick, using a sharp knife or mandoline. Transfer the cucumber slices to a fine-mesh strainer set over a bowl. Sprinkle with ½ teaspoon of the kosher salt and toss gently to coat. Let the cucumbers sit and drain for 30 to 60 minutes, tossing occasionally to help release excess moisture.
Finely chop the fresh dill and chives. Once the cream cheese is softened, add the minced dill and chives to the bowl along with the mayonnaise, remaining ½ teaspoon kosher salt, and black pepper. Stir and fold the mixture until everything is well incorporated and smooth.
To assemble, spread about 1½ tablespoons of the herbed cream cheese mixture onto one slice of sandwich bread using an offset spatula or butter knife. Leave a ½-inch border around the edges for clean presentation. Layer approximately 15 cucumber slices in an overlapping pattern across the cream cheese.
Top with a second slice of bread to complete the sandwich. Continue assembling sandwiches until you’ve used up all the filling—this recipe should yield about 7 full sandwiches.
Using a serrated knife, trim the crusts from each sandwich and set them aside for snacking. Then, cut each sandwich into your desired shape: halves for rectangles or triangles, or quarters for smaller servings. Arrange the finished cucumber sandwiches neatly on a platter or cake stand and serve chilled.