Bring a pot of water to a gentle boil, enough to fully submerge the eggs. Add 1 teaspoon of vinegar. Using a spoon, carefully lower the eggs into the water and hard-boil for 10 minutes. Then transfer the eggs immediately to an ice bath and let them cool for 5 minutes
Peel the eggs, then cut them in half. Separate the whites from the yolks. Finely mince the egg whites with a knife until small and uniform
Add the egg yolks to a mixing bowl along with Kewpie mayo, milk, salt, black pepper, and sugar. Mix until smooth and fully combined. Gently fold the minced egg whites into the yolk mixture. Taste and adjust seasoning as needed
Spread a thin, even layer of butter on one side of each shokupan slice. Spoon the egg salad onto one slice, slightly mounding more filling toward the center. Top with the second slice of shokupan, buttered side down.
Trim off the crusts with a sharp knife, and then, optionally, wrap the sandwich in parchment paper and refrigerate for 5 to 10 minutes to help the egg salad set so that it doesn't spill out when you cut it. Cut the sandwich diagonally and serve. Enjoy!
