Begin by preparing the white rice so it will be ready alongside the stir-fry. For ease of slicing, place the steak in the freezer for 30 minutes before cutting. In a mixing bowl, thoroughly combine the sauce ingredients, ensuring the sugar is fully dissolved, and set aside. Heat a large skillet over medium and pour in 1 tablespoon of oil. Add the broccoli florets and sauté for 4 to 5 minutes, keeping the lid partially on and stirring intermittently, until the broccoli turns bright green and reaches a crisp-tender texture. Remove from the pan. For softer broccoli, splash in 2 tablespoons of water before covering to allow steam cooking. Turn the heat to high and add the remaining tablespoon of oil. Spread the beef in a single layer and cook undisturbed for 2 minutes per side or until fully cooked, testing a piece for doneness. Pour the prepared sauce into the skillet, then lower the heat to medium-low and allow it to simmer for 3 to 4 minutes, or until thickened. Return the broccoli to the pan and stir well to incorporate. If the sauce appears too thick, dilute with 1 to 2 tablespoons of water. Serve the stir-fry hot over steamed white rice.