Cook the lo mein noodles according to package instructions. Drain and set aside.
In a small bowl, mix together soy sauce, oyster sauce, cornstarch, water, sesame oil, black pepper, and red pepper flakes (if using). Set the sauce aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak 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 remaining 2 tablespoons of vegetable oil. Add the minced garlic and ginger, and stir-fry for about 30 seconds until fragrant.
Add the broccoli florets to the skillet and stir-fry for 2-3 minutes until they are bright green and tender-crisp.
Return the beef to the skillet and pour the sauce over the beef and broccoli. Stir well to combine and cook for an additional 2 minutes until the sauce thickens.
Add the cooked lo mein noodles to the skillet and toss everything together until the noodles are well coated with the sauce.
Serve hot, garnished with sliced green onions.