Open out the thick part of the thigh so it's an even thickness and season lightly with salt and pepper. Toss with potato starch in a bag, then pat off the excess.
Heat a generous amount of oil in a frying pan over medium heat. Lay the chicken skin-side down and fry 2–3 minutes without moving it, until the skin is deep golden and crisp.
Meanwhile, stir together the soy sauce, mirin, sake, and sugar until the sugar dissolves.
Flip the chicken and cook the other side 1–2 minutes, then wipe the excess oil from the pan with a paper towel.
Pour in the sauce and let it bubble over medium heat, spooning it over the chicken until it reduces to a glossy glaze.
Rest a minute, slice into strips, and pour any remaining sauce over the top. Serve with shredded cabbage and rice.