Combine chicken pieces, soy sauce, rice vinegar, garlic, ginger, five-spice powder, white pepper, salt, and cayenne pepper in a large bowl. Let marinate for 10 minutes.
Heat oil in a deep-fryer or large saucepan to 400 degrees F (200 degrees C).
Whisk egg in a small bowl until smooth. Pour tempura batter mix into a second small bowl. Dip chicken pieces one at a time into the egg, then dredge in tempura batter mix, shaking off any excess. Lower chicken pieces carefully into the hot oil in batches. Fry until chicken is golden brown, 5 to 8 minutes. Transfer to a plate lined with paper towels to drain. Repeat with remaining chicken.
Serve chicken sprinkled with basil leaves, green onions, white pepper, and salt.
