If your wings are whole, use a sharp knife or kitchen shears to cut through the joints and separate each wing into a drumette and a flat. Pat every piece very dry on all sides with paper towels.
Transfer the dry wings to a large mixing bowl. Add 1 teaspoon kosher salt, black pepper, garlic powder, grated ginger, and mirin. Add the egg white and toss until every piece is evenly coated. Cover and refrigerate for 30 minutes.
In a wide, shallow dish, whisk together the potato starch, cornstarch, and remaining 1/2 teaspoon kosher salt. Toss the wings one at a time in the starch mixture, pressing firmly, then shake off excess. Rest on a wire rack for 10 minutes.
Add gochujang, gochugaru, honey, ketchup, soy sauce, rice vinegar, sesame oil, minced garlic, and water to a small saucepan. Whisk until smooth, then simmer over medium-low heat for 3 to 4 minutes until glossy and slightly thickened. Remove from heat and keep warm.
Pour neutral oil into a Dutch oven or heavy pot to a depth of 2 to 3 inches. Clip a deep fry thermometer to the side and heat over medium-high heat to 350°F. Set up a clean wire rack over a baking sheet next to the stove.
Carefully lower 5 to 6 wing pieces into the hot oil. Fry for 10 to 12 minutes, turning occasionally, until the coating is pale golden and the chicken is cooked through. Lift out and place on the wire rack. Repeat with remaining wings, bringing oil back to 350°F between batches.
Let all the fried wings rest on the rack for at least 10 minutes. During this rest, moisture from inside the chicken moves to the surface and evaporates, which sets up an extra crisp second fry.
Raise the oil temperature to 375°F. Fry the wings again in small batches for 3 to 4 minutes, until deep golden brown and very crunchy. Return to the wire rack to drain for 1 minute.
Place the hot wings in a large, clean mixing bowl. Pour the warm sauce over the top and toss quickly until every piece is glossy and evenly coated. Transfer to a serving platter and sprinkle with toasted sesame seeds and sliced green onions. Serve right away.