Step 1

Place potatoes in a large pot of salted cold water. Bring to a boil and cook until potatoes are tender, 15 to 20 minutes. Add carrots during the last 3 minutes of cooking. Drain and set aside.

Step 2

Place cucumber slices in a strainer and sprinkle with salt, coating the slices. Let sit for 10 to 15 minutes. Thoroughly rinse cucumbers and transfer to a stack of paper towels or a dry kitchen towel. Give them a good squeeze until most of the moisture is removed. This is an important step if you don't want to end up with a runny dressing.

Step 3

Cut hard-boiled eggs in half, and set aside 1/2 of 1 yolk. Cut egg whites and remaining yolks into small pieces.

Step 4

Place potatoes and carrots in a large bowl. Mash gently by pressing down with the back of a spoon until mostly mashed, but still a bit chunky. Mix in chopped egg, cucumber, red onion, apple, and black pepper.

Step 5

Whisk mayonnaise, gochujang, sesame oil, and ginger together in a bowl; fold into the potato mixture.

Step 6

Grate reserved egg yolk over the potato salad, and refrigerate for at least 1 hour before serving.