Cut the cucumber into thin, lengthwise slices that fit the width of your bread. Sprinkle lightly with salt and let sit on paper towels for about 10 minutes.
Mix the cream cheese, mayonnaise, mustard, dill, soy sauce, and black pepper in a small bowl until smooth and creamy.
Pat the cucumber slices really well with paper towels to remove as much moisture as possible. This little step helps keep the sandwiches from getting soggy.
Spread the cream cheese mixture on one side of 2 bread slices. Arrange a layer of cucumber on one slice, then place the other slice on top, cream cheese side down.
Spread more cream cheese mixture on top, add another layer of cucumber, and cover with a third slice of bread spread with cream cheese on the bottom side. Repeat with the remaining 3 bread slices.
Cut each stack into 6-9 little sandwiches using a sharp knife. Add a cocktail toothpick to each one, garnish with fresh dill and serve right away.