Cut the chicken thighs into 5 cm (about 2-inch) pieces and season lightly with salt and freshly ground black pepper.
Grate the ginger and garlic until fine.
In a bowl, combine grated ginger, grated garlic, soy sauce, mirin, sake and sesame oil to make the marinade.
Place the chicken and the marinade in a zip-top bag or airtight container and refrigerate for 1 hour.
Pour neutral oil into a deep saucepan to come halfway up the sides and heat to 160°C (320°F); use a thermometer to check the temperature.
Mix the cornstarch (or potato starch) and all-purpose flour in a shallow bowl.
One piece at a time, dredge the marinated chicken in the starch-flour mixture until evenly coated and place on a tray.
Fry the chicken pieces in the 160°C (320°F) oil for about 2 minutes until very light brown; transfer to a wire rack placed over a tray.
Strain the oil through a fine-mesh sieve if needed, then increase the oil temperature to 180°C (356°F).
Return the chicken to the hot oil and fry for about 1 minute or until golden brown and crisp.
Drain briefly on the wire rack, then serve with Kewpie mayonnaise and lemon wedges.