This is a tartar sauce you can make in a frying pan. You don't need to boil an egg, let it cool and peel it before mashing it!
I made a tartar sauce that doesn't require boiled eggs.
In short, just make your eggs sunny-side up, chop them up, and mix with the seasonings. Don't worry about the browned parts of the eggs. Just stick it all in together.
Enjoy Japanese food around the world.