Boil eggs in water for 10 minutes. After boiling, soak the eggs in cold water and peel the shells once fully cooled.
Cut the eggs with an egg slicer, reserving four large slices. Place the rest of the eggs in a bowl, add ¾ of the miso mayonnaise, and mix together while coarsely mashing the eggs.
Spread the remaining ¼ of the miso mayonnaise on bread slices. On two of the bread slices, arrange the reserved egg slices in the center of the bread in a single overlapping layer.
Cover the sliced eggs with egg and miso mayonnaise mixture and top with torn lettuce and remaining bread slices.