Prepare the potatoes: Wash, peel, and cut 2 small to medium potatoes into approximately 1-inch (3 cm) pieces. Soak them in water (not included in the ingredient list) for 5 minutes.
Cook the potatoes: Drain the water and place the potatoes in a heat-resistant bowl. Cover loosely with plastic wrap and microwave for 5 minutes. Insert a toothpick—if it comes out soft, the potatoes are ready. If not, microwave for an additional minute, or until they become soft.
Mash and season: Discard or wipe any excess water from the bowl. Mash the potatoes with a fork or masher while they’re hot. Add 1 tablespoon vinegar, ¼ teaspoon kosher salt, and ¼ + ⅛ teaspoon ground black pepper, then mix well. Let them cool in the fridge while preparing the other ingredients.
Prepare the vegetables: Mix 1 ¼ cup water and 2 teaspoon kosher salt to create salted water. Thinly slice ½ cucumber into coins and ¼ medium onion into thin slices. Soak them in the salted water for 10 minutes. After soaking, squeeze out the excess moisture with your hands.
Cut the ham: Slice 1 slice ham into 0.2-inch (0.5 cm) strips.
Combine the ingredients: Once the potatoes have cooled, add the squeezed cucumbers and onions, ham, and 4 tablespoons kewpie mayonnaise. Mix well. Taste and adjust with salt and pepper as needed.