Prepare udon noodles by blanching in boiling water for 1-2 minutes until loosened, then drain and set aside.
In a small bowl, combine soy sauce, oyster sauce, mirin, grated ginger, and minced garlic to create the stir-fry sauce.
Heat vegetable oil in a large wok or non-stick skillet over medium-high heat.
Add sliced chicken breast and cubed tofu to the wok; stir-fry for 5-6 minutes until chicken is cooked through and tofu edges are golden.
Add shredded cabbage and julienned carrots to the wok, sautéing for 2 minutes until vegetables are slightly softened.
Add the prepared udon noodles and the sauce mixture to the pan.
Toss all ingredients vigorously over high heat for 2-3 minutes until noodles are evenly coated and heated through.
Garnish with sliced green onions and serve immediately.