Whisk together the mirin, soy sauce, and sesame oil. Set aside.

Prepare Noodles:

Soak the frozen noodles in warm water until softened and all the noodles have separated. Drain and drizzle with 1 teaspoon sesame oil.

Pat the duck dry and score the skin in diagonal lines. Season all over with salt and pepper. Transfer the duck to a skillet, skin-side down, and turn the heat to medium. Cook for 8-9 minutes or until the fat has rendered and the skin is browned and crispy. Adjust the heat as necessary to keep the skin from burning. Flip and cook an additional 3-5 minutes or until the duck reaches 135ºF for medium rare. Transfer to a cutting board and rest for 5-10 minutes before slicing thinly.

Heat the neutral cooking oil and the remaining 1 tablespoon sesame oil in a wok or a skillet over medium high heat until hot. Add the shallot, garlic, and minced pepper and cook for 30-45 seconds or until fragrant. Add the shaved purple sweet potato and the cabbage and cook for 5-6 minutes, stirring occasionally until the vegetables begin to char slightly.

Pour in the sauce and scrape up any browned bits stuck to the bottom of the wok or skillet. Bring to a boil and add the noodles. Toss to coat and cook for 1-2 minutes or until the noodles are completely coated and warmed through. Turn off the heat.

Arrange the sliced duck on top of the udon and sprinkle the duck yaki udon with shichimi togarashi. Enjoy!