Toss the thinly sliced flank steak with 1 tablespoon reduced-sodium soy sauce, 2 teaspoons cornstarch, and 1 teaspoon neutral oil until every slice has a thin, even coating. Set aside while you mix the sauce. The beef should look lightly coated and moist without sitting in liquid.

Whisk the beef broth, 3 tablespoons reduced-sodium soy sauce, oyster sauce, brown sugar, 2 teaspoons cornstarch, toasted sesame oil, and rice vinegar until the cornstarch is completely dispersed. Keep the sauce near the stove and whisk it again immediately before adding it to the skillet.

Heat 1 tablespoon neutral oil in a 12-inch skillet over medium-high heat. Add the broccoli and toss for about 30 seconds. Add 2 tablespoons water and cover for 2 minutes. Uncover and cook for another 1 to 2 minutes, tossing occasionally, until the broccoli is bright green and crisp-tender. Transfer it to a plate.

Return the skillet to medium-high heat and add the remaining 1 tablespoon neutral oil. Spread half of the beef in a single layer. Sear for 60 to 90 seconds without moving it, then turn and cook for another 30 to 60 seconds, until browned around the edges. Transfer to the plate and repeat with the remaining beef. The beef does not need to be fully finished because it returns to the skillet in the sauce.

Reduce the heat to medium. Add the garlic and ginger and stir for 20 to 30 seconds, just until fragrant without browning. Whisk the sauce again, pour it into the skillet, and cook for 45 to 90 seconds, stirring, until glossy and lightly coating the spatula. Return the beef and broccoli and toss for 30 to 60 seconds, until evenly coated and heated through. Verify the thickest beef strips reach at least 145°F. Remove from the heat and let the stir-fry stand for 3 minutes before serving.