To prepare the tartar sauce, add the boiled egg, celery, scallion, mayonnaise, mustard, lemon zest, and lemon juice to a bowl and stir to combine. Add salt and white pepper to taste.
To make the nanban sauce, add the soy sauce, sake, sugar and ginger to a small saucepan and bring to a boil over high heat. Continue boiling for 1 minute and then turn off the heat and stir in the vinegar.
Add 2-inches of oil to heavy bottomed pot and heat to 340 degrees F (170 C) and prepare a wire rack and pan.
Trim any excess fat off the chicken and lightly salt and pepper.
Dust the chicken with flour.
Beat the egg in a bowl until uniform and then dip the chicken in the egg to thoroughly coat.
Gently lower the egg coated chicken skin-side down into the hot oil and then drizzle a little of the remaining egg onto the tops of each piece of chicken. The egg will quickly "bloom" and spread out.
Use tongs or chopsticks to fold the egg back over the chicken.
Fry the chicken until it's golden brown and cooked through (about 6-8 minutes). You'll want to flip the chicken over a few times, but be careful not to break the crust off off the chicken.
Dip the fried chicken in the sauce, flipping it over a few times to coat it evenly.
Slice and serve the chicken with the tartar sauce.