In a bowl, combine the cucumber with ¼ teaspoon kosher salt and mix well. Let it sit for 5 minutes until it sweats out water. Strain and squeeze out excess moisture.
Crack open the hard-boiled eggs and separate the yolks from the whites. Chop up the egg whites. Set aside. Grate an egg yolk for garnish: Press 1 egg yolk through a sieve (or wire strainer) with a wooden spoon. Set the other 2 egg yolks aside.
Rinse the potato chunks in cold water to remove excess starch and place them in a heavy-bottomed pot. Add ½ cup water and a pinch of salt. Cook for 20 minutes over medium high heat.
Remove from the heat. Drain any excess water, and put the cooked potato back to the pot. Cover and simmer for 1 or 2 minutes over very low heat, to remove more moisture. Uncover.
Mash the hot potato with a wooden spoon or a potato masher for 30 seconds and add the 2 cooked egg yolks and the egg whites. Keep mashing until well mixed.
Add the squeezed cucumber, ¼ teaspoon ground white pepper, and rice syrup. Mix it well with a wooden spoon. Add the mayonnaise and mix well. Cool it down at room temperature and keep it in the refrigerator. Serve cold as a side dish or snack.
Make a sandwich: Spread a scoop of chilled gamja-salad over a fresh leaf of lettuce, between two toasted pieces of bread. Serve or pack in a lunch with some fruit.
