Pat the chicken wings thoroughly dry with paper towels. In a large mixing bowl, toss the wings with neutral oil, salt, and black pepper until evenly coated.

In a small saucepan, combine the soy sauce, mirin, sake, brown sugar, minced garlic, and grated ginger. Whisk together until the sugar dissolves. Bring the mixture to a gentle simmer over medium heat, stirring occasionally.

In a small separate bowl, whisk together the cornstarch and water to create a smooth slurry. Once the sauce in the saucepan is simmering, slowly whisk in the cornstarch slurry. Continue to simmer and whisk for 1-2 minutes until the sauce thickens to a glossy consistency that coats the back of a spoon. Remove from heat and set aside.

Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper or foil, and place a wire rack on top (this helps for extra crispiness). Arrange the seasoned chicken wings in a single layer on the wire rack, ensuring they don't touch.

Bake for 20 minutes, then carefully flip the wings. Continue to bake for another 15-20 minutes, or until the wings are golden brown, crispy, and cooked through (internal temperature reaches 165°F / 74°C).

Preheat your air fryer to 375°F (190°C). Arrange a single layer of seasoned wings in the air fryer basket without overcrowding. Air fry for 10 minutes, then flip each wing. Continue to air fry for another 8-12 minutes, or until golden brown and crispy. Work in batches if necessary to avoid overcrowding.

Once the wings are cooked (using either method), immediately transfer them to the large mixing bowl. Pour about 3/4 of the prepared teriyaki sauce over the hot wings and toss gently with tongs until all wings are well coated and glistening.

Serve immediately, garnished with toasted sesame seeds and thinly sliced green onions, if desired. You can offer the remaining teriyaki sauce on the side for dipping.