Whisk 1 1/2 tablespoons soy sauce, 1 tablespoon honey, garlic, and ginger together in a large glass or ceramic bowl. Add chicken and toss to evenly coat. Cover the bowl with plastic wrap and marinate in the refrigerator for 8 hours to overnight.

Remove chicken from marinade and shake off excess. Discard remaining marinade.

Beat egg in a bowl until smooth. Add panko bread crumbs to a shallow bowl. Dip chicken into beaten egg. Lift up so excess egg drips back in the bowl. Press into panko until completely coated. Place the breaded chicken, unstacked, onto a plate. Repeat with remaining chicken.

Heat oil in a deep fryer or large saucepan to 350 degrees F (175 degrees C). Lower chicken carefully into the hot oil in batches. Fry until golden brown, about 5 minutes. Transfer to paper towels to drain. Repeat with remaining chicken.

Whisk Japanese mayonnaise, mirin, 2 tablespoons honey, Dijon mustard, and 1 tablespoon soy sauce together in a bowl; pour sauce over chicken.