Start by peeling and cutting potatoes into 2-inch chunks, then place them in a pot of cold salted water and bring to a boil. Simultaneously, place eggs in another pot of cold water and bring to a boil. Once the egg water boils, remove from heat and let eggs sit for 12-13 minutes to achieve creamy, jammy yolks. Meanwhile, boil potatoes until completely tender when pierced with a fork, about 12-15 minutes depending on size. When potatoes are done, drain thoroughly and return to the pot.
While potatoes and eggs cook, prepare all vegetables: finely dice the apple, mince the onion, thinly slice the scallion (keeping white and green parts separate), dice the cucumber into small pieces, and julienne or finely dice the carrot. For the cucumber, toss the diced pieces with a pinch of salt and let sit for 2-3 minutes, then squeeze out excess moisture with your hands or a clean kitchen towel—this prevents the salad from becoming watery. In a small bowl, whisk together mayonnaise, Dijon mustard, sugar, lemon juice, and a few grinds of black pepper to create the dressing base.
Transfer the cooked eggs to an ice bath (bowl of ice water) and let cool for about 10 minutes until completely chilled. This stops the cooking process and makes them easier to handle. While eggs cool, gently mash the hot potatoes in their pot using a potato ricer or fork until mostly smooth with just small lumps remaining—I prefer leaving them slightly chunky for better texture rather than making them completely creamy. Let the potatoes cool to room temperature, about 5 minutes, before combining with other ingredients.
Peel the cooled eggs, then separate the whites from the yolks; chop the egg whites into small pieces and reserve the yolks for garnish. Transfer the cooled mashed potatoes to a large mixing bowl, then add the chopped egg whites, diced apple, minced onion, white parts of scallion, prepared cucumber, carrot, raisins, and the dressing mixture from Step 2. Fold everything together gently but thoroughly until well combined, being careful not to overmix which can make the salad gluey. Taste and adjust seasoning with salt and black pepper as needed.
Transfer the salad to a serving bowl or plate. Press the reserved egg yolks through a fine-mesh strainer directly over the top of the salad to create delicate strands of golden garnish—this adds both visual appeal and bursts of rich flavor. Scatter the reserved green parts of scallion over the top as a fresh finishing touch. I like to chill the salad for at least 15-20 minutes before serving, as the flavors meld beautifully and it reaches the ideal cold temperature.