Whisk the soy sauce, ginger and brown sugar, add the chicken and refrigerate for 45 minutes to 2 hours.
Combine the rice flour, cornstarch, sesame seeds and salt in a wide bowl.
Drain the chicken well, press each thigh into the rice-flour mixture and rest the coated pieces on a rack for 8 minutes.
Heat the vegetable oil in a deep heavy pot to 350°F and fry 2 thighs at a time for 6 to 8 minutes, turning once and holding the oil between 335°F and 350°F, until the crust is crisp and the chicken reaches 165°F.
Drain the chicken on a clean wire rack and rest it for 5 minutes.
Toast the buns, spread both halves with mayonnaise and assemble each sandwich with 1 fried thigh and 1/4 cup cucumber slices.