In a bowl, toss the sliced beef with soy sauce and cornstarch. Let it sit while you prep the other ingredients—this helps tenderize the beef and give it a velvety texture when cooked.
In a small bowl, whisk together soy sauce, oyster sauce, hoisin sauce, brown sugar, sesame oil, ginger, red pepper flakes (if using), and water. Set aside.
Heat 1 tablespoon of oil in a large skillet or wok over medium-high heat. Add the beef and cook for 2–3 minutes until browned and just cooked through. Remove and set aside.
Add the remaining oil to the skillet. Add the broccoli and stir-fry for 3–4 minutes until it begins to soften. Stir in the garlic and cook for 30 seconds.
Return the beef to the skillet. Add the cooked noodles and pour in the sauce. Toss everything together and cook for 2–3 minutes until the sauce thickens slightly and coats everything evenly.
Remove from heat and serve hot. Garnish with green onions or sesame seeds if desired.