Prep the wings
Cut each chicken wing at its 2 joints, resulting in 3 parts per wing. Discard the wingtip (the entire third part), which will burn when deep-frying. Lightly season the chicken with salt and pepper. Transfer to a large bowl and set aside.
Sauce
Add the tobanjan, garlic, sugar, miso, soy sauce, sake, and mirin to a saucepan and place over high heat. Cook, stirring constantly, until the sugar and miso dissolve and the sauce comes to a boil. Transfer the sauce to a large mixing bowl and set aside.
Fry
Place a cast-iron skillet on a burner and fill with vegetable oil to a height of at least 1 inch. Attach a deep-fry (or "candy") thermometer to the side of the skillet. Near the skillet, set up a tray lined with newspaper or paper towels to drain the cooked wings. Turn the heat to high and heat the oil to 350°F.
While the oil is heating, add the katakuriko to the bowl with the chicken wings and toss until all the wings are evenly coated.
When the oil reaches 350°F, shake the excess katakuriko off the wings and carefully lay them in the oil. Cook in batches as needed — never use more than half the surface area of the oil, or the temperature will drop. Check the oil with the thermometer while the wings cook and regulate the heat to hold a constant 350°F.
Cook the wings for about 7 minutes, until cooked through and golden. They will float to the surface when done. Transfer to the paper-lined tray to drain.
Finish
When all the wings have been cooked, add them to the bowl with the sauce. Toss for about 1 minute, until the wings are evenly coated. Transfer to a serving platter, garnish with the sesame seed, and serve immediately.