Bring a pot of water to a boil. Gently add the eggs into the water to cook. Cook 1 egg for 6 minutes then remove it and place it into a bowl of ice water. Cook the remaining eggs for another 2 minutes then place them into the ice water to cool. Peel all the eggs.
Slice the 4 eggs that were boiled for 8 minutes in half. Remove the egg yolks from the whites and add them into a bowl. Roughly mash the yolks with a fork. Mix in the kewpie mayo, dill, chives, grated red onion, dijon mustard, and granulated sugar. Chop the egg whites into small pieces then mix them into the egg salad. Season with salt and black pepper to taste.
Lay 2 slices of the milk bread onto a cutting board. Slice the egg that was cooked for 6 minutes in half, lengthwise. Place each half onto the center of a slice of milk bread with the cut side facing down. Spread the egg salad mixture onto each slice of bread, going over the jammy egg. Sandwich with the remaining slice of bread on top.
Use a serrated knife to cut off the crusts then cut the sandwich in half. Try to aim for the center of the jammy egg yolk to get the perfect cross section. Enjoy!