Prepare the beef by patting the thinly sliced flank steak dry with paper towels, then place it in a medium bowl.
Season the beef with the fine sea salt and freshly ground black pepper, then sprinkle 1 tablespoon of cornstarch over the beef and toss until the slices are evenly coated.
In a small bowl or measuring jug, whisk together the low-sodium soy sauce, beef broth or stock, brown sugar, rice vinegar, and 1 tablespoon of cornstarch until completely smooth with no lumps; set this sauce mixture aside.
Heat 1 tablespoon of the vegetable oil in a large skillet or wok over medium-high heat until the oil is shimmering but not smoking.
Add the coated beef to the hot skillet in a single layer, cooking in batches if necessary, and sear for 2 to 3 minutes per side until the slices are browned on the outside and just cooked through; transfer the cooked beef to a plate and set aside.
In the same skillet, add the remaining 1 tablespoon of vegetable oil, then add the broccoli florets and cook for 2 minutes, stirring often, until they start to turn bright green.
Pour in the 2 tablespoons of water, quickly cover the skillet with a lid, and steam the broccoli for another 2 to 3 minutes until crisp-tender, then remove the lid and let any excess moisture cook off.
Reduce the heat to medium, add the minced garlic and grated ginger to the broccoli, and cook for about 30 seconds, stirring constantly, until fragrant but not browned.
Give the prepared sauce mixture a quick stir, then pour it into the skillet with the broccoli, stirring well and letting it come to a gentle simmer.
Simmer the sauce for 2 to 3 minutes, stirring frequently, until it thickens into a glossy, smooth coating that clings lightly to the broccoli.
Return the cooked beef and any accumulated juices to the skillet, tossing everything together until the beef and broccoli are evenly coated in the thickened sauce and heated through, about 1 to 2 minutes.
Taste the beef and broccoli mixture and adjust the seasoning if needed by adding a little more soy sauce or a pinch of salt to suit your preference.
To serve, divide the warm cooked rice evenly among four bowls, creating a bed of rice in each one.
Spoon the saucy beef and broccoli mixture generously over the rice in each bowl, making sure to include plenty of sauce.
Garnish each beef and broccoli bowl with sliced green onions and a light sprinkle of toasted sesame seeds, then serve immediately while hot.