Bring a pot of water to a boil and add the large eggs. Boil for 7 minutes and 30 seconds for medium-boiled or 9 minutes for hard-boiled eggs. Transfer eggs to an ice bath for at least 5 minutes.

Peel the cooled eggs and mash yolks and whites in a bowl. Add milk, Kewpie mayo, sugar, salt, and black pepper, mixing until combined. Refrigerate for 10 minutes.

Cut off the crusts of shokupan slices. Spread softened butter on one side of each slice. Place two medium-boiled egg halves on two slices and add a generous layer of the egg mayo mixture.

Place the remaining buttered shokupan slices on top, buttered side down. Press the sandwich to compress the filling slightly.

Slice the assembled sandwich diagonally and serve immediately with green tea or pickled vegetables.