1 1/2 pounds russet potatoes, about 3 large potatoes, peeled and quartered
2 Persian cucumbers, thinly sliced crosswise
2 teaspoons rice wine vinegar
6 tablespoons homemade or store-bought Japanese mayonnaise, such as Kewpie
1/2 teaspoon Japanese hot mustard
1 small carrot, quartered and thinly sliced crosswise
1/4 red onion, thinly sliced
2 hard boiled eggs, chopped
1 scallion, white and light green parts only, chopped
Place potatoes in a large pot and add enough cold water to cover by 1 inch. Season generously with salt, set over high heat, and bring to a boil. Reduce to a simmer and cook until potatoes are easily pierced with a fork, 10 to 15 minutes. Drain potatoes and transfer to a large bowl. Let cool.
Meanwhile, place cucumbers in a bowl and sprinkle 1/2 teaspoon salt. Mix well, then let stand for 10 minutes. Drain any accumulated water, then gently squeeze cucumbers with paper towels to blot up any excess liquid.
In a small bowl, stir together rice vinegar, mayonnaise, and hot mustard until well mixed.
Mash potatoes with a masher or a large fork, allowing some small lumps to remain. Add cucumbers, carrots, onions, eggs, scallions, and mayonnaise mixture. Mix well and season with salt. Serve right away. The salad can be refrigerated up to 1 day.