Prepare udon noodles according to package instructions, drain, and set aside.
In a small bowl, whisk together soy sauce, oyster sauce, mirin, and dark soy sauce to create the stir-fry sauce.
Heat vegetable oil in a wok or large skillet over high heat.
Add sliced chicken and cubed tofu, searing until the chicken is fully cooked and tofu edges are golden brown.
Add garlic and ginger to the wok, sautéing for 30 seconds until fragrant.
Toss in shredded cabbage and julienned carrots, stir-frying for 2 minutes until vegetables are tender-crisp.
Add the prepared udon noodles to the pan.
Pour the sauce mixture over the ingredients and toss vigorously for 2 minutes until the noodles are well-coated and heated through.
Drizzle with sesame oil and garnish with sliced green onions before serving.