Lay the two slices of white sandwich bread flat on a clean surface.
Spread 1 tablespoon of mayonnaise evenly on one side of each bread slice.
Place 2 slices of cheddar cheese on one slice of bread over the mayonnaise.
Add 2 slices of tomato on top of the cheese.
Place 2 leaves of iceberg lettuce over the tomato slices.
Add 2 slices of cucumber on top of the lettuce.
Sprinkle salt and black pepper to taste over the cucumber slices.
Cover with the second slice of bread, mayonnaise side down, to complete the sandwich.
Press gently to hold the sandwich together.
Cut the sandwich diagonally into two halves if desired and serve immediately.