Cook the eggs. Bring a saucepan of water to a gentle boil. Carefully lower in the eggs and maintain a gentle boil for approximately 11–12 minutes, until the yolks and whites are fully set. Cooking times vary with egg size; check that both yolks and whites are firm.
Cool and peel. Transfer the eggs to a bowl of ice water for about 8 minutes. Peel and pat dry. Cooling makes the eggs easier to handle before mixing the filling.
Make the creamy filling. Cut the eggs in half. Scoop out the yolks and mash them in a bowl with Japanese mayonnaise, sugar, salt, and pepper. Chop the whites into small pieces and fold them into the yolk mixture. Taste and adjust the seasoning. Mashing the yolks separately produces a creamier filling while preserving texture from the whites.
Prepare the bread. Lay out eight slices of soft milk bread. Trim off the crusts if desired for a neat presentation. Do not toast the bread; its softness is part of the sandwich.
Assemble and serve. Divide the egg mixture evenly among four bread slices, keeping a small border around the edges. Top with the remaining slices, press gently, and cut each sandwich in half or into thirds. Serve promptly or refrigerate until serving. Keep prepared sandwiches cold if not eating them right away.
