Slice the steak very thinly against the grain. For easier slicing, place the beef in the freezer for 15–20 minutes first.Toss the sliced beef with 2 tablespoons cornstarch until lightly coated.
In a small bowl, whisk together soy sauce, beef broth, honey or brown sugar, oyster sauce if using, sesame oil, cornstarch, rice vinegar, and black pepper.Set aside.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Add broccoli and 2 tablespoons water. Cover and cook for 3–4 minutes, until the broccoli is bright green and crisp-tender. Transfer broccoli to a plate.
Add a little more oil to the skillet if needed. Add beef in a single layer and cook for 2–3 minutes, stirring occasionally, until browned and mostly cooked through. (Avoid overcrowding the pan. Cook the beef in batches if needed.)
Add garlic and ginger to the skillet. Cook for about 30 seconds, until fragrant.Pour in the sauce and stir until it thickens and coats the beef, about 1–2 minutes.
Return broccoli to the skillet and toss everything together until coated in sauce and heated through. Serve over rice and top with sesame seeds, green onions, or red pepper flakes if desired.