Step 1: Prepare the Vegetables

1. Cucumber: Slice the cucumber as thinly as you can. A mandoline slicer is excellent for this. Place the slices in a small bowl, sprinkle with 1 teaspoon of salt, and mix well. Let it sit for 15-20 minutes. The salt will draw out excess water, which is crucial for preventing a watery salad and ensuring the cucumber stays crisp.
2. Onion: Slice the yellow onion very thinly. Place the slices in a separate bowl and cover with cold water. Let it soak for 10-15 minutes. This process removes the harsh, raw bite of the onion, leaving only its sweet, mild flavor.
3. Carrot: Slice the carrot into thin rounds or half-moons. We will cook this with the potatoes.
4. Ham: Cut the sliced ham into small, bite-sized squares or strips. Set aside.

Step 2: Cook the Potatoes, Eggs, and Carrots

1. Potatoes: Peel the Yukon Gold potatoes and cut them into uniform 1-inch cubes. Place them in a large pot and cover with cold, salted water (use 1 tablespoon of salt).
2. Eggs: Gently place the 3 whole eggs into the same pot with the potatoes. This is an efficient way to hard-boil them.
3. Boil: Bring the pot to a rolling boil over high heat. Once boiling, reduce the heat to a steady simmer.
4. Add Carrots: After about 5 minutes of simmering, add the sliced carrots to the pot.
5. Cook Times:

   • Remove the eggs after they have cooked for 10-12 minutes in the simmering water. Immediately transfer them to an ice bath to stop the cooking process. This makes them easier to peel and prevents the dreaded green ring around the yolk.
   • Continue cooking the potatoes and carrots until the potatoes are very tender and can be easily pierced with a fork, typically about 15-20 minutes total. The carrots should be tender-crisp.

Step 3: Assemble the Salad Base

1. Drain: Once the potatoes and carrots are cooked, drain them thoroughly in a colander. Let them steam dry for a minute to remove any excess moisture.
2. Mash: Transfer the hot potatoes and carrots to a large mixing bowl. While they are still hot (this is important for a creamy texture), use a potato masher or a large fork to mash them. Do not over-mash. The goal is a “half-mashed” texture. Aim for about 70% mashed and 30% small, soft chunks remaining.
3. Season the Mash: While the potato mixture is still warm, season it with the rice vinegar, sugar, ½ teaspoon of salt, and black pepper. The warm potatoes will absorb the seasonings much more effectively than cold ones. Mix gently to combine. Let this mixture cool down for about 15-20 minutes on the counter.

Step 4: Finalize the Mix-ins

1. Squeeze Vegetables: Go back to your prepped cucumber and onion. Squeeze the cucumber slices firmly with your hands to remove all the excess water you can. You’ll be surprised how much comes out. Drain the onions and pat them dry with a paper towel.
2. Peel and Chop Eggs: Peel the cooled hard-boiled eggs. Roughly chop two of the eggs and add them to the cooled potato mixture. Reserve the third egg for garnish if you wish, or chop it and add it in as well.

Step 5: Combine and Chill

1. Add Everything: To the bowl with the cooled, seasoned potato mash, add the squeezed cucumber, dried onion, chopped ham, and chopped eggs.
2. Introduce the Kewpie: Add the ¾ cup of Kewpie mayonnaise. Gently fold all the ingredients together with a spatula until everything is well combined. Be careful not to overmix, as this can make the salad gummy.
3. Taste and Adjust: This is your final chance to perfect the flavor. Taste the salad and add more salt, pepper, or even a touch more Kewpie mayo if you feel it needs it.
4. Chill: Cover the bowl with plastic wrap and refrigerate for at least 1 hour before serving. This step is non-negotiable! Chilling allows all the flavors to meld together and deepens the taste of the salad significantly. It will taste much better after it has rested.