Trim any excess fat from the steak and slice it very thin across the grain. In a medium bowl toss the beef with 1 tsp cornstarch, 1 tsp oil and a few cracks of black pepper. Let rest 8–10 minutes while you prep the veg.
Bring a medium pot of water to a boil. Add the broccoli florets and blanch for 60–90 seconds until bright green and just tender. Immediately drain and plunge into iced water to stop cooking; drain again and set aside.
Whisk the sauce: combine the soy sauce, rice vinegar and honey in a small bowl. In a separate small cup mix 1 tbsp cornstarch with 2 tbsp water until smooth and set both mixtures aside.
Heat a large wok or heavy skillet over high heat until very hot. Add 1 tbsp neutral oil and swirl. Working in a single layer cook half the beef for 45–60 seconds per side until just browned but not fully cooked through. Remove to a plate and repeat with the remaining beef, adding the remaining 1/2 tbsp oil if needed.
Lower the heat to medium-high and return the pan to the stove. Add the minced garlic and ginger and stir for 20–30 seconds until aromatic (don’t let it burn).
Add the blanched broccoli and the cooked beef back to the pan. Pour the soy-honey mixture over everything and stir to combine.
Give the cornstarch slurry a quick stir and drizzle it into the hot pan while stirring constantly. Cook for 1–2 minutes until the sauce thickens and coats the beef and broccoli.
Remove the pan from heat and stir in the toasted sesame oil. Taste and adjust with a pinch of pepper or a splash more soy if needed. Sprinkle sliced green onions and sesame seeds on top before serving.
Serve immediately over steamed rice or cauliflower rice for a lower-carb option.