Place luncheon meat cubes, processed cheese sauce, pimientos, and sandwich spread in a blender; pulse to blend into a smooth mixture, stopping often to scrape down blender sides. Transfer spread to a bowl.
Spread the mixture onto 15 slices of white bread; top each with a slice of whole wheat bread. Press sandwiches together lightly and cut off crusts. Slice sandwiches in half diagonally to make triangles; sprinkle sandwiches with parsley flakes and top each sandwich half with a piece of sliced cucumber.
