Peel the cucumber and slice it thinly into rounds. Set aside.
In a mixing bowl, combine the softened cream cheese, softened butter, chopped dill, salt, and pepper. Mix until smooth and well combined.
Lay out the slices of bread on a clean surface.
Spread a generous layer of the cream cheese mixture on one side of each slice of bread.
Place a layer of cucumber slices on half of the bread slices, ensuring they cover the entire surface.
Top with the remaining slices of bread, cream cheese side down, to create sandwiches.
If desired, cut off the crusts using a knife or sandwich cutter, and cut each sandwich into quarters or halves for serving.
Serve immediately or refrigerate until serving.
For added flavor, sprinkle the cucumber slices with a bit of salt and let them sit for 5 minutes to release excess moisture before assembling the sandwiches.