Pat the beef dry with paper towels and slice it thinly against the grain.
Place the beef in a bowl and toss it with cornstarch, soy sauce, garlic powder, and black pepper. Let it rest for about 10 minutes.
In a small bowl, whisk together the soy sauce, beef broth, honey or brown sugar, oyster sauce, rice vinegar, minced garlic, grated ginger, and sesame oil.
In a separate bowl, mix 1 teaspoon cornstarch with 1 tablespoon cold water to make a smooth slurry. Set aside.
Heat a large skillet or wok over medium-high heat. Add a small amount of olive oil, followed by the broccoli and 1 tablespoon of water.
Cover and cook the broccoli for about 2–3 minutes, until bright green and slightly tender. Transfer it to a plate.
Add the remaining olive oil to the hot skillet. Cook the beef in a single layer, working in batches if necessary.
Cook the beef for about 2–3 minutes per side, or until browned and cooked through.
Return the broccoli to the skillet and pour in the prepared sauce. Stir everything together and simmer gently for 1–2 minutes.
Stir the cornstarch slurry again and pour it into the skillet while stirring.
Continue cooking for another 1–2 minutes, until the sauce thickens and coats the beef and broccoli.
Remove from the heat and garnish with sliced green onions and sesame seeds if desired.
Serve immediately over steamed white rice, brown rice, or noodles.