Peel and boil the potatoes, then mash them.
Chop the boiled egg into small pieces.
Slice the cucumber thinly, sprinkle with salt, and squeeze out the moisture.
Finely chop the carrot and blanch it lightly.
In a bowl, mix potatoes, eggs, cucumber, carrot, mayonnaise, salt, and pepper together.
Place the potato salad on a slice of bread and cover with another slice.
Cut into pieces for easy eating.