together the softened cream cheese and mayonnaise until the mixture is completely smooth and spreadable. You want a fluffy, creamy texture with no lumps.
Lay out the slices of white sandwich bread on a clean counter or cutting board. If the bread is very soft, you can leave it in a single layer for a few minutes to dry just slightly, which makes spreading easier without tearing.
Spread a thin but even layer of the cream cheese mixture over each slice of bread, going all the way to the edges so the sandwiches seal nicely once cut.
Arrange a single layer of cucumber slices over half of the bread slices, covering the surface but not piling them too thickly. The cucumbers should sit flat so the sandwiches stay neat when cut.
Top each cucumber-covered slice with a second slice of bread, cream cheese