In a medium bowl, combine ¾ cup cream cheese, ¼ cup sour cream (or mayonnaise), 2 tablespoons chopped dill, and a pinch of kosher salt. Blend until smooth and creamy, about 1-2 minutes.

Lay 8 slices of bread flat and generously spread the herbed cream cheese mixture onto one side of each slice.

Wash and thinly slice half of an English cucumber into rounds, ensuring they are about 1/8-inch thick. Arrange the cucumber slices on half of the cream cheese-covered bread.

Place the other half of the cream cheese-covered bread slices on top of the cucumbers, spread side down. Gently press each sandwich together to hold the layers.

Trim the crusts off each sandwich to achieve a clean look.

Cut each sandwich into four small pieces. Place them on a serving platter.

If not serving immediately, cover the platter with plastic wrap and refrigerate for about 15 minutes.