Slice the beef: Freeze the steak for 15–20 minutes to firm it up, then slice thinly against the grain. Pat dry with paper towels.
Make the sauce: In a bowl, whisk soy sauce, rice vinegar, honey (if using), garlic, ginger, cornstarch, and a pinch of red pepper flakes. Set aside.
Prep the broccoli: Cut into bite-size florets.
If using thick stems, peel and slice them thin so they cook evenly.
Heat the pan: Set a large skillet or wok over medium-high heat. Add 1 tablespoon oil until shimmering.
Sear the beef: Cook the beef in two batches to avoid crowding. Sear 1–2 minutes per side until browned but still tender.
Transfer to a plate.
Cook the broccoli: Add a splash of oil if the pan is dry. Toss in broccoli and the white parts of the green onions. Stir-fry 3–4 minutes until crisp-tender.
Add a tablespoon of water and steam for 30–60 seconds if needed.
Combine and sauce: Return the beef and any juices to the pan. Pour in the sauce and toss to coat. Cook 1–2 minutes until the sauce thickens and everything is glossy.
Finish: Drizzle with sesame oil and sprinkle the green onion tops.
Taste and adjust seasoning with more soy, vinegar, or chili.
Serve: Spoon over your choice of base. Garnish with sesame seeds and a squeeze of lime if you like.