In a mixing bowl, combine softened cream cheese with sour cream or mayonnaise, dill, and kosher salt. Blend for about 2 minutes until creamy.

Trim crusts off the sandwich bread slices. Wash and slice the cucumber thinly, aiming for approximately 1/8-inch thickness.

Spread the herbed cream cheese mixture on one side of each slice of bread.

Layer thin cucumber slices on half of the cream cheese-covered bread slices, then top with remaining bread slices.

Cut each sandwich into quarters and arrange on a serving platter.

Chill assembled sandwiches in the refrigerator for about 15 minutes if making ahead of time.