Start the rice first. Combine the rinsed rice, 420 ml water, and 1/2 tsp salt in a 3-quart / 2.8 L saucepan and bring to a boil. Cover, reduce the heat to low, and cook for 15 minutes, then take it off the heat and leave it covered until serving.
Pat the flank steak dry and slice it across the grain into 6 mm strips about 5 cm long. Toss the strips in a bowl with 1 tbsp cornstarch, 1 tbsp soy sauce, and 1 tbsp water, then let them marinate for 15 minutes.
While the beef marinates, whisk the sauce in a small bowl: 80 ml soy sauce, 60 ml water, brown sugar, oyster sauce, 1 tbsp cornstarch, and sesame oil. Cut the broccoli into 4 cm florets and mince the garlic and ginger.
Heat 1 tbsp oil in a 30 cm / 12-inch cast-iron skillet over high heat for 3 minutes, until it shimmers. Add half the beef (about 340 g) in a single layer and sear for 90 seconds without moving it, until browned on the bottom. Flip and cook 1 minute more, then move it to a plate. Add 1 tbsp oil and repeat with the second batch.
Lower the heat to medium-high and add the last 1 tbsp oil, the garlic, and the ginger. Stir for 30 seconds until fragrant. Add the broccoli and 60 ml water, cover, and steam for 3 to 4 minutes until bright green and just tender.
Uncover and whisk the sauce again, since the cornstarch settles. Pour it in and simmer for 1 to 2 minutes until it coats the back of a spoon. Return the beef and its juices to the pan and toss for 1 minute, until the strips are browned outside with a trace of pink in the thickest ones, 145 F / 63 C.
Spoon the beef and broccoli over 1 cup of rice per plate. Top with the sliced scallions and sesame seeds, and serve right away.