This recipe closely mirrors what I would call the best egg salad sandwich I've ever eaten in my life, widely available at "conbini"/convenience stores across Japan. My personal favorite one was at 7-Eleven, but they all have the same idea: super-smooth eggs that don't shy away from mayo, in between soft white bread.
I use a food processor to fluff up the egg salad, and add salt to taste as I puree. Use pepper sparingly; it should be super subtle. (It's better to use pepper that hasn't been freshly ground.) While milk bread is ideal, any soft white bread should do the trick; just make sure the crusts are off. If you don't have kewpie mayo, regular mayo will do (but kewpie mayo is great—and you'll get good use out of a bottle, available online and at most Asian markets). —Nikkitha Bakshani
You can boil eggs however you like, but I recommend a method that still yields a bright, yellow yolk. Bring a pot of water to a boil, and add a splash of rice vinegar. Place the eggs in the water and boil, uncovered, for 9 minutes. Remove and place in a large bowl of ice water. Peel the eggs in the water (it comes off easier). Cut the hard-boiled eggs in halves or quarters and place in a food processor.
While eggs are boiling, cut the crusts off two slices of bread.
Add the mayo to the food processor, and a little bit of salt. Puree for a few seconds. Taste, add more salt and pepper, if necessary. You won't be processing it for too long—just enough for the egg salad to look smooth and unified.
Spread over one slice of bread, so that there's a thick layer. You might not want to spread it too close to the edges, as the pressure of your fingers on the sandwich might make the filling ooze out a bit. (But it's a pretty oozy sandwich, so don't fret.) Top with the other slice and cut in half, gently, with a sharp knife. You can also enjoy this open-faced; that's not the 7-Eleven way but it's still good. There will be leftover egg salad; set it aside, refrigerate, and use within a few days.