In a medium pot, bring enough water to a rolling boil over high heat. Optionally, add a teaspoon of salt and a tablespoon of white vinegar to help ease peeling. Once boiling, gently lower six room-temperature eggs into the water, being careful not to crack them. Cover the pot, reduce the heat to medium-high, and cook the eggs for precisely 13 minutes for perfect hard-boiled eggs.

After 13 minutes, immediately transfer the boiled eggs into an ice bath to stop the cooking process. Allow the eggs to sit in the ice bath for about 5-10 minutes until completely chilled.

Once cool, remove the eggs from the ice bath and gently tap them on a hard surface to crack the shell. Peel the eggs from the less pointed end using a spoon.

Separate the egg yolks from the whites, placing the yolks into a mixing bowl. Push the yolks through a fine sieve to create a velvety base. Finely chop the egg whites and add them to the bowl.

In the bowl with the egg yolk mixture, add Japanese mayo, salt, sugar, and black pepper. Mix until smooth.

If using brioche buns, slice them about 95% through. If using white sandwich bread, lay out 12 slices on a clean surface.

Spoon an equal portion of the creamy egg salad into each bun or slice of bread, pressing gently to keep everything in place.

Optionally, sprinkle dried parsley over the top and serve fresh and warm.