Boil the eggs for 12–13 minutes, then transfer them to cold water. Peel once cooled.
Separate the yolks and whites. Roughly chop the egg whites.
Add the mayonnaise, milk, sugar, salt, and pepper to the yolks. Mix well until smooth.
Add the chopped whites and gently mix, keeping some texture.
Spread a thin layer of butter and Japanese mustard on the inside of the bread slices.
Add a generous amount of the egg filling and sandwich with another slice of bread.
Gently press the sandwiches and let them rest for about 5 minutes. Cut into easy-to-eat pieces and serve.
