Boil potatoes. Place clean halved potatoes in a pot. Cover them with cold salted water. Bring water to boiling on high heat. Reduce the heat to minimum and simmer for about 20 minutes until cooked. Taste it after first 15 minutes and adjust timing if needed. Strain water and let potatoes cool uncovered to evaporate extra moisture. If cooked in advance, store in covered container refrigerated.
Soft boil eggs. Place eggs in a pot and fill it with cold water. Bring water to boiling on high heat. Reduce the heat to minimum and simmer for about 10 minutes. Strain water and fill the pot with ice cold water. Let eggs cool down completely, then shell them carefully. If cooked in advance, store in covered container refrigerated. Slice or chop them before serving.
Wash, deseed, and dice cucumber.
Wash, slice, and dice radishes.
Dice ham. Chop scallions, chives, and greens.
When all the ingredients are ready for serving, you can mix and season them before portioning. Or you can serve them buffet style, so everybody can make their own version of soup. Serve liquid ingredients separately. Garnish with greens and eggs.