Cook the Potatoes: Boil the potato chunks in salted water until they are tender, about 10-12 minutes. Drain the potatoes and set them aside to cool slightly.

Prepare the Vegetables: While the potatoes are cooling, slice the cucumber thinly and sprinkle with a pinch of salt. Let it sit for about 5 minutes, then squeeze out any excess moisture. Dice the carrots into small pieces and blanch them in boiling water for 2-3 minutes, then drain and set aside.

Mix the Ingredients: In a large mixing bowl, add the cooled potatoes and mash them slightly with a fork, leaving some small chunks for texture. Add the chopped hard-boiled eggs, diced ham, corn, blanched carrots, and cucumbers.

Make the Dressing: In a small bowl, whisk together the Japanese mayonnaise, rice wine vinegar, sugar (if using), salt, and black pepper. Adjust seasoning to taste.

Combine: Pour the dressing over the potato mixture and gently fold everything together until evenly coated. Be careful not to overmix to preserve the texture of the potatoes and vegetables.

Chill and Serve: Let the salad chill in the refrigerator for at least 30 minutes before serving to allow the flavors to meld. Serve cold or at room temperature.