Cook the udon noodles according to package instructions. Drain and set aside.
In a bowl, combine the sliced flank steak, soy sauce, oyster sauce, and cornstarch. Mix well and let marinate for about 15 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated beef and cook until browned, about 3-4 minutes. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the broccoli, bell pepper, and carrots. Stir-fry for about 5 minutes until the vegetables are tender-crisp.
Add the garlic and ginger to the skillet and stir-fry for an additional 1 minute until fragrant.
Return the beef to the skillet and add the cooked udon noodles. Drizzle with sesame oil and toss everything together until well combined and heated through. Season with salt and pepper to taste.
Serve hot, garnished with sliced green onions and sesame seeds if desired.