In a medium bowl, combine the soy sauce, sake, grated ginger, grated garlic, and sesame oil. Add the chicken thigh pieces and toss well to coat, then let it marinate at room temperature for 15 minutes.

Drain any excess marinade from the chicken pieces. Place the potato starch in a shallow bowl and coat each piece of chicken thoroughly, shaking off any excess starch so only a thin, dusty layer remains.

Fill a heavy-bottomed pot or Dutch oven with about 2 inches of vegetable oil and heat over medium-high heat until it reaches 325°F (160°C).

Carefully lower the chicken pieces into the hot oil in batches to avoid overcrowding, and fry for 3 to 4 minutes until the exterior is light golden and cooked through. Transfer to a wire rack to rest for 3 minutes.

Increase the oil temperature to 350°F (180°C). Return the chicken to the hot oil in batches and fry for an additional 1 to 2 minutes until the skin turns deeply golden brown and feels incredibly crispy.

Remove the chicken from the oil, drain on paper towels for 1 minute, and serve immediately with fresh lemon wedges on the side.