Prepare the beef by patting the flank steak dry with paper towels, then slicing it thinly against the grain into bite-sized strips.

Place the sliced beef in a bowl, add 1 tablespoon cornstarch, the fine sea salt, and black pepper, and toss until the beef is evenly coated.

In a small bowl, whisk together the low-sodium soy sauce, honey, water, minced garlic, grated ginger, rice vinegar, toasted sesame oil, and 1 teaspoon cornstarch until smooth; set this honey garlic sauce aside.

Bring a medium pot of water to a boil, add the broccoli florets, and blanch for 1 to 2 minutes until they turn bright green and slightly tender, then drain well and set aside.

Heat 2 tablespoons of the vegetable oil in a large skillet or wok over medium-high heat until hot but not smoking.

Add half of the coated beef strips in a single layer and sear for about 1 to 2 minutes per side until browned but not fully cooked through, then transfer to a plate and repeat with the remaining beef, adding a little more vegetable oil if needed from the remaining 1 tablespoon.

Lower the heat to medium, add any remaining vegetable oil to the skillet if the pan looks dry, and pour in the prepared honey garlic sauce, stirring constantly for 1 to 2 minutes until it begins to thicken and bubble.

Return the seared beef and any accumulated juices to the skillet, tossing in the thickened honey garlic sauce until the beef is evenly coated.

Add the blanched broccoli florets to the skillet and gently stir-fry everything together for 2 to 3 minutes until the broccoli is heated through and the beef is just cooked to your liking.

Taste the sauce and adjust if needed, then remove the skillet from the heat and sprinkle the sliced green onions and toasted sesame seeds over the beef and broccoli.

Serve the honey garlic beef and broccoli immediately over warm cooked white rice, spooning extra sauce from the pan over each serving.