Cook the udon noodles according to package instructions. Drain and set aside.
In a large skillet or wok, heat the vegetable oil over medium-high heat.
Add the sliced beef to the skillet and stir-fry for about 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add the onion, garlic, bell pepper, and broccoli. Stir-fry for about 5 minutes until the vegetables are tender-crisp.
Return the beef to the skillet and add the cooked udon noodles.
Pour in the soy sauce, oyster sauce, black pepper, and sesame oil. Toss everything together until well combined and heated through, about 2-3 minutes.
Serve hot, garnished with chopped green onions.