Get a pot of salted water boiling (large enough to fit the 4 potatoes)
Peel and cube potatoes. Boil until soft (12-15 minutes).
While potatoes are steaming hot, mash them roughly.
Stir in 1 tablespoon of rice vinegar.
Stir in 1 pinch of sugar.
Once cooled slightly, fold in kewpie mayonnaise. Start by folding in half a cup. If it still looks dry, add more mayonnaise. It should look glossy and rich.
Mash egg into the warm potatoes.
Refrigerate.
When ready to serve, fold in cucumber and red onion.