Cook the lo mein noodles according to the package instructions, then drain and set aside.
In a mixing bowl, whisk together soy sauce, oyster sauce, cornstarch, water, sesame oil, and black pepper until smooth.
Heat 2 tablespoons of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak and stir-fry for 3-4 minutes until browned. Transfer to a plate and keep warm.
Add the remaining tablespoon of oil to the skillet. Sauté minced garlic and ginger for about 30 seconds.
Add broccoli florets and stir-fry for 2-3 minutes until vibrant green and tender-crisp.
Return the cooked beef to the skillet and pour the sauce over the beef and broccoli. Cook for an additional 2 minutes until the sauce thickens.
Add the lo mein noodles to the skillet, tossing until heated and coated in sauce.
Sprinkle chopped green onions on top before serving.