The original recipe is from justhungry.com, a great website for basic Japanese recipes. See her version for more in detail notes about packaging the potato salad for potlucks or picnics. I used Japanese mayo once and then regular mayo + a bit of sugar the other time. You can also add diced Fuji apples for additional sweetness and crunch.
6-7 medium red potatoes, well scrubbed
1 small carrot
1 seedless cucumber (I use Persian)
Salt and pepper
3/4 to 1 cup of mayonnaise, Japanese or regular (if regular, add a teaspoon or two of sugar)
Boil the unpeeled carrot and potatoes in their skins until tender (you can poke a skewer through a potato without any resistance). Boil the egg until hard boiled at the same time.
In the meantime, slice the cucumber and the onion very thinly. Sprinkle both with a little salt, and let sit for a while (15+ minutes) until the vegetables exude their juices. Squeeze firmly to get rid of the juices.
When the potatoes and carrot are done, drain peel them while still hot (holding each in a kitchen towel to peel them helps). Cut the potatoes into small pieces, and slice the carrot. Toss with a little salt and pepper and leave to cool.
Peel the hard boiled egg and chop up finely. If you’re adding in the Fuji apple, this is when you can peel the apple and dice it up.
When the potatoes and carrot mixture has cooled to room temperature, mix in the cucumber, onion, egg, and mayonnaise. Cover with plastic wrap and refrigerate for at least an hour before serving.