Step 1

Marinate the beef and make the sauce: Cut the steak crosswise (with the grain) into 2- to 3-inch-wide strips. Cut each strip across the grain into 1/4-inch-thick pieces. Place the beef in a medium bowl; set aside.

Step 2

Whisk the remaining ingredients in a small bowl until the cornstarch and sugar are fully dissolved. Transfer 2 tablespoons of this sauce mixture to the bowl of beef and toss to coat the meat; set the beef and remaining sauce aside.

Step 3

Make the stir-fry: Fill a large frying pan halfway with water and bring to a boil over medium-high heat. Add the broccoli, cover, and cook, stirring halfway through, until crisp-tender, about 3 minutes total. Drain and set aside.

Step 4

Wipe the pan dry and heat over medium-high heat until a drop of water vaporizes immediately on contact. Drizzle in 1 teaspoon of the oil, then add half of the beef and spread into an even layer. Cook undisturbed until the beef begins to sear, about 1 minute. Using a metal spatula, stir-fry until the beef is lightly browned but not cooked through, about 30 seconds more. Transfer to a large plate. Repeat with another teaspoon of oil and the remaining beef.

Step 5

Drizzle the remaining teaspoon of oil into the pan. Add the ginger and garlic, and stir-fry until the garlic is fragrant, about 30 seconds. Add the broccoli and beef and any accumulated juices, and stir to combine. Whisk the sauce again to recombine and dissolve the cornstarch, then add to the pan. Stir-fry until the beef is just cooked through and the sauce thickens and is glossy, 1 to 2 minutes. Transfer to a serving dish, sprinkle with the scallions and sesame seeds if using, and serve over rice.