Fill a large pot with plenty of water and bring it to a boil. Once boiling, reduce the heat to medium and carefully lower eggs into the water using a slotted spoon or ladle. Let them cook for at least 12 minutes.
Remove the boiled eggs from the pot, cool them under running water, and then peel them before cutting them in half to separate the yolks and whites. Mash the yolks in a bowl using a spoon or spatula, and dice the whites into cubes about ⅕ inch (5-6mm) in size.
Add seasonings (sugar, salt, pepper, and Japanese mayonnaise) to the bowl, and mix thoroughly with the yolks until the mixture reaches a creamy consistency, which should take a few minutes. Next, add the chopped whites and mix everything together.
Spread butter on one side of each slice of shokupan. Evenly spread the egg mixture on the buttered side of one slice, then sandwich it with another slice of shokupan buttered on one side. Repeat this process to make the desired number of tamago sando.
Cut off the crusts and slice the shokupan diagonally or horizontally. For cleaner cuts, it is recommended to wipe the knife with a paper towel between cuts.