Season the chicken with salt and let it stand for 15 minutes, then dust it with 1/4 cup cake flour.
Whisk the mayonnaise and sriracha together and refrigerate the sauce.
Heat the canola oil in a deep heavy pot to 350°F before mixing the batter.
Beat the egg with club soda in a cold bowl, add the remaining cake flour and cornstarch and stir only 8 to 10 times so small lumps remain.
Dip 2 cutlets in batter, let the excess fall away and fry for 5 to 7 minutes, turning once and keeping the oil between 340°F and 350°F, until pale gold, crisp and 165°F inside; repeat with the remaining cutlets.
Drain the chicken on a wire rack and rest it for 3 minutes.
Toast the buns and build each sandwich with spicy mayo, 1 tempura cutlet and 1/2 cup shredded lettuce.