Dice and deseed the cucumber into small pieces. Mix with 1/4 tsp of salt and let it sweat for 10 minutes. Cucumbers hold a lot of water and we don't want any of it leaking into the potato salad.
Hard boil your eggs however you want, but this is how I do it and they come out perfect every time: Bring a pot of water to a boil (enough to cover the eggs). Gently drop the eggs in and boil them for 7 minutes uncovered
Take the eggs out and let them cool before peeling. Keep the water boiling, add the potatoes and cover. Boil for 20 minutes on medium high heat
When the potatoes can be easily pierced with a chopstick, turn off the heat and drain
Let the potatoes rest for 5 minutes. Do not skip this step.
Add the egg whites and 1 1/2 yolks. You can just add all of the yolks if you don't care to garnish nicely at the end
Mash everything together until smooth
Add the kewpie mayo, rice syrup, and white pepper. Mix
Add the cucumber and apple last. Mix again
Finely grate the rest of the egg yolk over the potato salad
Serve at room temp or cold from the fridge. Keeps in the fridge for up to 4 days