In a bowl, whisk together the low-sodium soy sauce, 1/2 cup water, brown sugar, cornstarch, sesame oil, and rice vinegar until smooth.

Slice the flank steak thinly against the grain. Place the beef in a separate bowl, pour 2 tablespoons of the sauce mixture over it, and toss to coat. Let marinate for 15 minutes.

Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the broccoli florets and 2 extra tablespoons of water. Cover and steam for 3 to 4 minutes until crisp-tender, then remove the broccoli from the pan and set aside.

Wipe the skillet clean if necessary and heat the remaining 1 tablespoon of vegetable oil over high heat. Add the marinated beef in a single layer and sear for 1 to 2 minutes per side until browned and cooked through.

Add the minced garlic and ginger to the pan with the beef, stirring continuously for 30 seconds until fragrant.

Return the cooked broccoli to the skillet. Pour in the remaining sauce mixture and toss everything together.

Simmer for 1 to 2 minutes until the sauce thickens and evenly coats the meat and vegetables. Garnish with sesame seeds and serve immediately.