Peel the shrimp and leave the tails. Devein and rinse the shrimp. Cut a few shallow vertical slits at the bottom of the shrimp to keep them from curling up when you fry them. Pat the shrimp dry with paper towels and set aside.
Add all-purpose flour, salt, bonito flakes, egg, and milk in a bowl and whisk to combine well. Set the batter aside. If the batter is too thick, add a little bit more milk.
Pour the Panko breadcrumbs into a shallow plate.
Coat the shrimp evenly with the batter by holding the tail to dip, and then roll it into Panko. Give the shrimp a light press to ensure that the shrimp is entirely covered with the breadcrumbs. Repeat the same process for the remaining shrimp.
Fill a deep poy with vegetable oil and heat the oil to 340°F to 360°F (170°C to 182°C).
Deep-fry the shrimp until golden brown and crispy on both sides. Remove from the oil with a strainer, and drain on a plate lined with paper towels.
Prepare the dipping sauce. Cut the hard-boiled egg into small cubes, mix it with chopped onion and Japanese mayonnaise in a bowl. Finally, add salt and ground black pepper to taste.
Enjoy the shrimp hot with cold dipping sauce immediately.