Preparation: Start by cooking white rice, ensuring it is ready when the stir fry is done. For easier slicing, cover the steak and freeze it for 30 minutes before cooking.
Stir Fry Sauce: In a medium bowl, combine all the ingredients for the stir fry sauce. Stir well until the sugar is fully dissolved. Set the sauce aside for later use.
Heat a large skillet over medium heat and add 1 tablespoon of oil. Add the broccoli florets and sauté for 4-5 minutes, partially covered with a lid, stirring or tossing several times. Cook until the broccoli is bright green and crisp-tender. If you prefer softer broccoli, add 2-3 tablespoons of water before covering with the lid. Remove the cooked broccoli from the pan.
Increase the heat to high and add the remaining 1 tablespoon of oil to the skillet. Arrange the beef in a single layer and sauté for 2 minutes per side, or until cooked through.
Add the sauce to the skillet, then reduce the heat to medium-low and simmer for 3-4 minutes until it thickens. Add the broccoli and stir to combine. If desired, stir in 1-2 tablespoons of water to thin the sauce.
Sprinkle with green onions and sesame seeds.
Serve the stir-fry over white rice.