Prep the vegetables. Cut each vegetable to size, keeping types separate. Soak sweet potato in cold water 10 minutes, then dry. Pat everything completely dry on towels.
Mix the batter. Whisk flour, cornstarch, baking powder, salt, and white pepper together. In another bowl beat the cold egg, then whisk in the ice-cold club soda. Combine wet and dry and stir just 10 seconds — the batter should stay lumpy and thin. Set over ice.
Coat. Toss the panko with the oil in a shallow dish. Dip one vegetable piece at a time in the batter, let excess drip off for two seconds, then press gently into the panko to coat. Coat only enough for one basket at a time.
Air fry. Preheat to 375°F for 3–5 minutes and spray the basket. Arrange pieces in a single layer without touching. Spray the tops until no dry panko shows. Cook 6–12 minutes depending on vegetable (see chart), flipping and re-spraying at the halfway point, until golden and fork-tender.
Finish. Salt immediately, rest 2 minutes on a wire rack, and serve with tentsuyu or soy dipping sauce, topped with sliced green onion and black sesame seeds.