Wash potatoes and cucumbers thoroughly and slice thinly.
Steam the potatoes and mash them.
Boil the eggs in boiling water for 10 minutes and peel.
Chop the boiled eggs, then mix with mashed potatoes, cucumber, mayonnaise, salt, and pepper.
Spread the mixture evenly over two slices of bread.
Cover with another slice of bread to complete the sandwich.
Cut into bite-sized pieces.