Heat a little oil in a pan over medium heat. Sauté the white onion, cabbage, carrot, and garlic until softened and the moisture evaporates, about 5 to 7 minutes. Let cool slightly, then transfer to a bowl. Add ground chicken, green onion, ginger, sesame oil, soy sauce, salt, and pepper. Mix until well combined. Cover and refrigerate.

In a mixing bowl, combine the flour, boiling water, and salt. Knead for 7 to 8 minutes until the dough is smooth and elastic. Wrap in plastic and let rest for 30 minutes. Roll out thinly with a pasta machine or rolling pin, then cut into circles.

Place a teaspoon of filling in the center of each wrapper. Lightly moisten the edges with water, fold, and pinch to create small pleats forming the classic chicken gyoza shape.

In a pan over medium heat, warm a little oil. Add garlic and lemongrass and cook until fragrant. Stir in sugar, miso, soy sauce, and yuzu juice until smooth. Gradually add cold butter, stirring continuously to create a silky emulsion.

Heat the vegetable oil in a small saucepan. In a separate bowl, combine garlic, chili flakes, soy sauce, and sugar. Pour the hot oil over the mixture and stir to combine.

Heat a little oil in a nonstick pan over medium heat. Arrange the chicken gyoza in a single layer and cook until the bottoms are golden and crispy. Pour in a few tablespoons of water, cover, and steam for 5 minutes. Uncover and cook until the water evaporates and the bottoms crisp up again.

Spread the miso butter sauce on a plate, arrange the chicken gyoza on top, and drizzle with chili oil. Finish with a scattering of green onions and serve immediately.