In a large pot, bring water to boil over high heat. Add the udon noodles and cook until barely tender. Drain and set aside.
While the udon is cooking, thinly slice and set aside all the vegetables.
In a small bowl, whisk together the soy sauce, sake, and mirin.
Place a wok or large pan over medium high heat. Add the sesame oil.
Once heated, add the thinly sliced pork and cook, stirring often until just browned.
Add the onion, garlic, and carrot and cook (adding a little more sesame oil if needed), until starting to soften.
Stir in the mushrooms, light parts of green onions, and cabbage.
Once the cabbage has wilted and vegetables are tender, toss in the udon noodles and the soy sauce mixture until well coated.
Heat everything through, adjust flavors with additional soy sauce or salt if needed, and serve immediately topped with dark green onion pieces, dried bonito flakes, and beni shoga.