Season the chicken pieces with salt, pepper, and soju, and let sit for 10 minutes.
Toss the chicken in starch until evenly coated, shaking off the excess.
Heat the oil to 160°C / 325°F. Fry the chicken in batches for 6 to 7 minutes, until pale gold and cooked through, then drain on a rack.
Let the oil come back up to 190°C / 375°F, then fry the chicken again in batches for 2 to 3 minutes, until deep golden brown and audibly crisp when tapped.
While the chicken rests, combine the mulyeot, soy sauce, brown sugar, garlic, ginger, gochujang, and water in a wide pan and simmer over medium heat for 2 minutes, until it thickens slightly and coats a spoon.
Add the fried chicken to the pan and toss quickly over low heat until every piece is coated in the glaze.
Transfer to a plate immediately, scatter with peanuts, chili, and sesame seeds before the glaze fully sets.