Marinate the Chicken: In a medium bowl, combine the thinly sliced chicken with 2 tablespoons of soy sauce and 1 tablespoon of cornstarch. Mix well to coat the chicken evenly and set aside to marinate for at least 10 minutes.
Prepare the Sauce: In a small bowl, whisk together the sauce ingredients: 1/4 cup soy sauce, 2 tablespoons oyster sauce, 1 tablespoon hoisin sauce, 1 tablespoon rice vinegar, 1 tablespoon honey or brown sugar, and 1 teaspoon chili garlic sauce (if using). Set aside.
Cook the Udon Noodles: Bring a pot of water to a boil. Add the fresh udon noodles and cook for 1-2 minutes, or according to package instructions, until just tender. Drizzle with a bit of sesame oil to prevent sticking and set aside.
Stir Fry the Chicken: In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium-high heat. Add the marinated chicken and stir fry for 4-5 minutes until fully cooked and slightly golden.
Sauté the Vegetables: In the same skillet, add the sesame oil. Add the sliced onion, red bell pepper, julienned carrot, and broccoli florets. Sauté the vegetables for 3-4 minutes until they are tender yet maintain a slight crunch. Then, incorporate the minced garlic and ginger, cooking for an additional 1-2 minutes until their aroma is released.
Combine Noodles and Chicken: Add the cooked udon noodles to the skillet along with the cooked chicken. Pour the prepared sauce over the noodles and vegetables. Toss everything together using tongs or a spatula, ensuring the noodles and vegetables are well coated with the sauce.
Finish and Serve: Continue stir frying for another 2-3 minutes until everything is heated through and the sauce has slightly thickened. Taste and adjust seasoning if necessary.