In a small bowl, whisk together the soy sauce, Worcestershire sauce, ketchup, oyster sauce, brown sugar, and sesame oil. Set aside.
In a large skillet or wok, heat 2 tablespoons of vegetable oil over medium-high heat. Add the chicken and sauté for about 5-7 minutes until golden brown. Remove from pan.
In the same skillet, add the ginger and garlic. Sauté for 1 minute until fragrant.
Add the onion, carrots, and bell pepper. Stir-fry for about 3-4 minutes until tender yet crisp.
Add the cabbage and stir-fry for an additional 2-3 minutes until wilted.
Toss in the chicken and yakisoba noodles. Pour the sauce over and stir well. Cook for 2-3 minutes until heated through.
Remove from heat, garnish with green onions, and serve hot.