In a medium bowl, combine the cream cheese, sour cream or mayonnaise, finely chopped dill, and a pinch of kosher salt. Blend until smooth and creamy.

Spread an even layer of the herbed cream cheese mixture on one side of each slice of sandwich bread.

On half of the prepared bread slices, arrange the thinly sliced English cucumbers in a slightly overlapping fashion.

Place the remaining slices of bread on top of the cucumber layers, spread side down, and press down lightly.

Using a serrated knife, trim off the crusts from all sides of each sandwich and cut each sandwich into quarters.

Arrange the cut sandwiches on a serving platter and garnish with extra dill or cucumber slices if desired.