Prepare the Cream Cheese Mixture: In a medium mixing bowl, combine softened cream cheese, sour cream or mayonnaise, finely chopped dill, and a pinch of kosher salt. Blend until smooth and creamy, about 2 minutes.

Spread the Cream Cheese: Use a butter knife to spread the herbed cream cheese mixture on one side of each slice of bread.

Slice the Cucumber: Rinse the cucumber and pat it dry. Thinly slice the cucumber into rounds, about 1/8-inch thick.

Assemble the Sandwiches: Layer cucumber slices over half of the cream cheese-coated bread slices, then top with the remaining slices, spread-side down.

Trim and Cut the Sandwiches: Trim the crusts off each sandwich and cut into quarters.

Serve or Store: Arrange sandwiches on a platter, garnish if desired, and cover with a damp paper towel if preparing ahead.