In a small mixing bowl, combine the ingredients for the yakisoba sauce—vegan mushroom sauce, ketchup, Tonkatsu or fruit & vegetable sauce, soy sauce, and sugar. Whisk until fully blended and smooth. Set aside.
Heat a wok or large skillet over medium-high heat. Add the sliced onions, white parts of the green onions, soy curls, and carrot. Stir-fry for about 1 to 2 minutes, until the onions begin to soften and become translucent.
Next, toss in the cabbage, bean sprouts, and sliced shiitake mushrooms. Continue stir-frying for another minute, allowing the vegetables to wilt slightly while still retaining some crunch.
Add the cooked yakisoba noodles and the green parts of the scallions to the pan. Stir everything together and continue frying for another minute to allow the ingredients to blend and heat through evenly.
Pour the prepared yakisoba sauce over the mixture and toss well until the noodles and vegetables are thoroughly coated and glossy with sauce.
Transfer the hot yakisoba to serving plates. Garnish with a generous pinch of aonori and serve alongside beni shoga for a vibrant, tangy contrast. Serve immediately while hot.