Prepare the Beef: Place sliced beef in a bowl; add soy sauce, sesame oil, garlic, and ginger. Let it sit for 10 minutes.
Cook the Beef: Heat oil in a large skillet or wok over medium-high heat. Stir in marinated beef and stir-fry for 3–4 minutes or until browned. Remove and set aside.
Stir-Fry the Broccoli: In the same pan (add a splash more oil if the pan looks dry), add the broccoli. Add the broccoli, and stir-fry for 4–5 minutes, or until just-tender but still crisp.
Stir Together & Simmer: Return the beef to the pan, sprinkle red pepper flakes, taste and season, and stir. Cook 2 minutes more to combine flavors.
Rest and Serve: Rest the dish for 5 minutes, then serve hot.