Prepare Ice Bath: Fill a large bowl with ice water and set it aside to chill the eggs after boiling.

Boil Eggs: Gently place the eggs into a saucepan filled with boiling water. Cook soft-boiled eggs for about 7 minutes or hard-boiled eggs for 10 minutes. After the time is up, turn off the heat and let the eggs sit in the hot water for an additional minute before transferring them to the ice bath for 2 minutes.

Mash Egg Salad: Once the eggs have cooled, carefully peel them under running water. In a mixing bowl, mash the peeled eggs using a fork until they reach a coarse consistency. Fold in sugar, salt, and freshly ground black pepper. Then fold in Japanese mayonnaise, adding a splash of milk if desired.

Assemble Sandwich: Spread a thin layer of unsalted butter on one side of each slice of Japanese milk bread. On one slice, generously spread the creamy egg salad, then top with another slice of bread, buttered side down.

Serve and Store: Trim the crusts for a cleaner presentation, then cut it in half diagonally. Serve immediately or wrap tightly in plastic wrap and refrigerate for up to 2 days.