Boil the potatoes with their skins on until cooked through.
Cool the boiled potatoes, peel off the skins, and mash them.
Thinly slice cucumber and carrot, sprinkle with salt to let them sweat, then remove excess moisture.
Finely chop the onion and soak in cold water to reduce its sharpness.
Mix the mashed potatoes with the prepared vegetables, mayonnaise, salt, and pepper until well combined.