Place the English cucumber on a cutting board and slice it as thinly as possible. A mandoline slicer works well for even slices.
Arrange the cucumber slices on paper towels and sprinkle lightly with flake sea salt and black pepper.
Let the cucumbers rest for 5 minutes to release excess moisture. For make-ahead preparation, allow them to sit for up to 30 minutes.
Spread the softened chive and onion cream cheese evenly over 4 slices of bread.
Layer the cucumber slices over the cream cheese, slightly overlapping them.
Sprinkle with additional flake sea salt and pepper if desired.
Add fresh dill for extra flavor and freshness.
Top with the remaining bread slices to complete the Cucumber Cream Cheese Sandwiches.
Remove the crusts from all sides of the sandwiches.
Cut each sandwich into quarters, triangles, or finger sandwiches before serving.