Thinly slice the flank steak against the grain and toss it with 1 tablespoon of cornstarch.
Bring a pot of water to a boil and blanch the broccoli for 2–3 minutes until bright green, then drain and set aside.
In a small bowl, whisk together soy sauce, brown sugar, hoisin sauce, garlic, ginger, sesame oil, and ½ cup water, then stir in 1 tablespoon of cornstarch to thicken.
Heat oil in a large skillet or wok over high heat.
Add the beef in a single layer and sear until browned and cooked through, about 3–4 minutes, then remove to a plate.
Pour the prepared sauce into the same pan and let it bubble until it thickens.
Return the beef and broccoli to the pan, tossing until everything is evenly coated in the sauce.
Garnish with sliced green onions and sesame seeds, then serve over rice or noodles.