In a medium bowl, toss the sliced beef with the cornstarch, 1 tablespoon of the soy sauce, and 1 teaspoon of the sesame oil. Let it marinate for at least 15 minutes while everything else gets ready.

Whisk the remaining 2 tablespoons of soy sauce with the beef broth, oyster sauce, and brown sugar in a small bowl until the sugar dissolves.

Bring a pot of water to a boil and add the broccoli for exactly 1 minute. Drain it right away. The broccoli should still be bright and firm, so do not walk away.

Heat 1 tablespoon of the vegetable oil in a large skillet or wok over high heat until it shimmers. Add half the beef in a single layer and let it cook undisturbed for about 2 minutes, until it is browned underneath. Flip the beef and cook about 1 minute more, then transfer it to a plate. Repeat with the remaining tablespoon of oil and the second half of the beef.

Reduce the heat to medium-high. Add the garlic and ginger to the same pan and stir for 15 seconds, until fragrant.

Add the blanched broccoli to the pan and toss for 1 minute so it picks up the garlicky oil and finishes cooking.

Return the beef and all its juices to the pan. Give the sauce one more whisk and pour it in. Stir until the sauce coats everything and thickens enough to gloss over the beef and broccoli, about 1 minute.

Take the pan off the heat and drizzle with the remaining teaspoon of sesame oil. Serve immediately over cooked white rice, sprinkled with sesame seeds if you like.