Boil the eggs: Bring a saucepan of water to a boil over high heat and carefully add 5 eggs. Boil the eggs for 10 minutes, then transfer them to a bowl of ice water and let them sit for 5 minutes before peeling.
Separate the egg yolks and whites: Peel the 5 boiled eggs, cut them in half, and place the egg yolks into a bowl while setting the egg whites aside on a chopping board.
Make the creamy yolk mixture: Mash the 5 egg yolks with 1/3 cup Japanese mayonnaise, 1/2 tsp sugar, 1 1/2 tbsp milk, and 1/4 tsp black pepper until smooth and creamy.
Chop the egg whites: Finely chop the 5 egg whites into small pieces using a knife.
Combine the egg filling: Add the yolk mixture to the chopped 5 egg whites and mix until evenly combined.
Assemble the sandwiches: Spread the egg filling evenly over 2 slices white bread, then top with the remaining 2 slices white bread to form 2 sandwiches.
Slice and garnish: Cut each sandwich in half and garnish with chopped or dried parsley if desired.