Prep the beef: Freeze the steak for 20–30 minutes to firm it up.
Slice thinly against the grain. Toss with 3 tablespoons cornstarch until lightly coated. Set aside while you prep the rest.
Make the sauce: In a bowl, whisk soy sauce, water/broth, brown sugar, 1 tablespoon cornstarch, rice vinegar, and chili-garlic sauce if using.
Keep it nearby.
Par-cook the broccoli: Blanch florets in boiling salted water for 1 minute, then drain and shock in cold water. Pat dry. Alternatively, stir-fry the broccoli in a teaspoon of oil for 2–3 minutes until bright green and crisp-tender.
Remove and set aside.
Heat the pan: Use a large skillet or wok. Add 1 tablespoon oil over medium-high to high heat until shimmering. Work in batches for the beef—crowding will steam it.
Sear the beef: Add a single layer of beef and let it sear undisturbed for 45–60 seconds, then stir-fry another minute until mostly browned but not fully cooked.
Remove to a plate. Repeat with remaining oil and beef.
Sauté aromatics: Lower heat slightly. Add garlic, ginger, and the white parts of the green onions.
Stir for 20–30 seconds until fragrant—do not burn.
Build the sauce: Give the sauce a quick stir, then pour it into the pan. Let it bubble for 30–60 seconds until it starts to thicken and turn glossy.
Combine: Return beef and broccoli to the pan. Toss to coat.
Stir-fry 1–2 minutes until the beef is just cooked through and the broccoli is heated. If using, finish with sesame oil.
Garnish and serve: Remove from heat. Top with green onion tops and sesame seeds.
Serve over warm rice or noodles. Squeeze a bit of lime if you like brightness.