Cook the lo mein noodles according to package instructions. Drain and set aside.
In a small bowl, mix the soy sauce, oyster sauce, cornstarch, beef broth, sesame oil, and black pepper. Set aside.
In a large skillet or wok, heat 2 tablespoons of vegetable oil 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 tablespoon of vegetable oil. Add the minced garlic and ginger, and stir-fry for about 30 seconds until fragrant. Add the broccoli florets and stir-fry for 2-3 minutes until they are bright green and tender-crisp.
Return the beef to the skillet, then pour the sauce mixture over the beef and broccoli. Stir well to combine and cook for an additional 2-3 minutes until the sauce thickens.
Add the cooked lo mein noodles to the skillet, tossing everything together until the noodles are well coated with the sauce. Cook for another minute to heat through.
Garnish with chopped green onions before serving.