Toss wings, 2 tbsp. each mirin and sake, the sesame oil, granulated sugar, salt, garlic, and ginger in a bowl; cover and chill 4 hours.
Combine remaining mirin and sake, the soy sauce, and turbinado sugar in a 4-qt. saucepan over medium heat; cook until reduced by half, about 1 hour.
Transfer sauce to a large bowl and cover with plastic wrap; keep warm.
Heat 2″ canola oil in a 6-qt. saucepan over medium until a deep-fry thermometer reads 320°.
Toss wings with potato starch, shaking off excess; working in batches, fry wings until crisp, about 4 minutes. Transfer wings to paper towels to drain.
Toss wings with reserved sauce; transfer to a platter and sprinkle with sansho. Serve with lemon wedges.