PREPARATION Step 1 In a medium saucepan, cover the potatoes with cold water by at least 1 inch. Add a few big pinches of salt. Bring to a boil over high heat. Gently lower the eggs into the pot. Cover, reduce to a bare simmer, and cook until the potatoes are tender and show no resistance when pierced with a knife or cake tester, 10 to 12 minutes. Drain the potatoes in a colander and spread in a single layer on a large rimmed baking sheet. Immediately sprinkle with vinegar and sugar. Set aside until completely cool, at least 15 minutes. Transfer the eggs to a bowl of ice water and peel when completely cool.

Step 2 Meanwhile, toss the cucumber with a big pinch of salt in the bottom of a large bowl and set aside until the potatoes are cool.

Step 3 When the potatoes are cool, add them to the bowl with the cucumber and lightly mash with the back of a fork until some bite-size chunks still remain.

Step 4 Add carrot, corn, radish, scallion, mayonnaise, mentaiko, lemon zest and juice. Squeeze the hard-boiled eggs through your clean fingers to break them up, or chop them with a knife and add them to the salad. Stir together and season with pepper, more salt, sugar, vinegar, lemon juice or mayonnaise, or a combination, to taste.

INGREDIENTS Yield: 4 to 6 servings

1 pound russet potatoes (about 2 whole large potatoes), peeled and cut into large chunks

Salt

2 eggs

1 tablespoon rice vinegar, plus more to taste

2 teaspoons sugar

1 small Japanese or Persian cucumber, or ½ an English cucumber (about 4 ounces), quartered lengthwise, seeds removed and discarded, and thinly sliced

1 small carrot (2 to 3 ounces), quartered lengthwise and thinly sliced

½ cup thawed frozen corn kernels or briefly boiled fresh corn kernels (optional)

¼ cup chopped radish (about 2 radishes; optional)

2 scallions, thinly sliced

5 tablespoons Kewpie mayonnaise (see Tip), plus more to taste

1 whole sac mentaiko or tarako (about 2 ounces)

1 teaspoon grated lemon zest

1 teaspoon fresh lemon juice, plus more to taste

Freshly ground black pepper