Combine all sauce ingredients in a small bowl.
To prepare your noodles from frozen, soak them in hot water for about a minute, and carefully loosen the noodles. Otherwise if you want to use packed udon noodles, then put in a pot with boiling water for 1-2 minutes until the noodles are loose. Drain them then set them aside.
Heat a wok or a large pan over medium heat and add vegetable oil together with the tofu, shrimp or any protein source that you prefer. Cook well and set aside.
In the same wok, add vegetable oil, onion, and cabbage, and sauté for a few minutes until the edges are golden brown, for about 3-4 minutes.
Add garlic, carrot, and mushrooms, and continue to cook for about 1 minute.
Now return your cooked tofu (or shrimp) and the udon noodles back in the wok
Add the sauce, and toss them together until the noodles are evenly coated and caramelized.
Garnish with sesame seeds and green onions and enjoy!