Bring a large pot of water to a boil. Cook the lo mein noodles according to package instructions, then drain and set aside.
In a small bowl, mix the soy sauce, oyster sauce, cornstarch, and water to create a sauce. Set this aside.
In a large skillet or wok, heat vegetable oil over medium-high heat. Add the sliced beef and season with salt and pepper. Cook until browned, about 3-4 minutes, then remove from the skillet and set aside.
In the same skillet, add minced garlic, ginger, and broccoli florets. Stir-fry for 3-4 minutes until the broccoli is bright green and tender-crisp.
Return the cooked beef to the skillet with the broccoli. Add the prepared sauce and sesame oil, stirring well to combine.
Toss in the cooked lo mein noodles, mixing everything together until the noodles are coated in the sauce and heated through, about 2 minutes.
Serve hot, garnished with sliced green onions if desired.