Bring a large pot of salted water to a boil. Add the chopped broccoli and cook 1–2 minutes until bright green and just tender, then transfer immediately to a bowl of ice water to stop cooking; drain and pat dry.
In a large bowl, whisk 2 tablespoons cornstarch with 2 tablespoons water to form a thin slurry. Add the beef strips and toss to coat evenly; set aside.
In a separate bowl, whisk together the remaining 1 tablespoon cornstarch with 1 tablespoon water, then add soy sauce, rice vinegar, brown sugar, minced garlic, sesame oil, and grated ginger; set the sauce aside.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat. Add the coated beef in a single layer and cook until no longer pink, about 3–5 minutes, stirring or turning as needed. Remove the beef and set aside.
Add the remaining 1 tablespoon vegetable oil to the skillet. Add the drained broccoli and cook 1–2 minutes until heated through and slightly crisp.
Return the cooked beef to the skillet, pour in the prepared sauce, and bring to a simmer. Cook 1–2 minutes until the sauce thickens and coats the beef and broccoli.
Serve immediately over rice or noodles and sprinkle with sesame seeds.