Make the spread by adding cream cheese, parsley, mayonnaise, chives, lemon zest and salt/pepper to a bowl and mashing until well combined.
Slice the cucumber into thin slices, about ⅛ of an inch.
To make each sandwich, take two pieces of bread and spread the cream cheese mixture evenly from crust to crust. Make sure to get a good layer everywhere on the bread, even the corners. Layer the cucumbers into 2-3 layers on one side of the bread to make sure every space is covered with a cucumber. Close the sandwich by firmly pressing the other cream cheese side down onto the cucumbers. Repeat this step to make 2 (or more) of these sandwiches.
Place the two sandwiches on top of each other and refrigerate for at least 1 hour- this will help set everything and it will be easier to cut.
Once the sandwiches are cold, use a serrated knife to evenly cut off the crust. Cut into rectangles "fingers" or diagonally for triangles.
Place nicely on a serving tray and enjoy.