Whisk together the marinade ingredients in a small bowl. Add the steak strips to a large bowl (or food storage bag) and pour the marinade over the steak. Toss to coat evenly. Marinade the steak for 1 hour in the fridge.
Once the marinating time is up, remove the steak from the fridge, and set aside. Make the stir fry sauce by adding all ingredients in a medium bowl and whisking until well combined. Set aside.
Add 1 tablespoon of oil into a large skillet placed over medium heat, and add in broccoli florets. Add 2 tablespoons of water (be careful, because the oil may pop) and cover with a lid. Cook, stirring occasionally, for about 5 minutes. You can add more water if needed to get the broccoli to your desired tenderness. Transfer the cooked broccoli to a bowl or plate and set aside.
With the same skillet still on medium heat, add 1 tablespoon of oil. Place a single layer of the steak in the pan and sear for 2-3 minutes. Then flip and sear on the other side for another 1-2 minutes.
Transfer the cooked steak to a plate and repeat with the remaining strips. You need to work in batches so the steak cooks quickly and gets a good sear. Overcrowding the pan will create too much moisture, and the steak will boil instead.
Reduce the burner heat to low. Add all of the cooked steak back into the pan along with the stir fry sauce. Cook until the sauce has thickened slightly, stirring occasionally.
Stir in the broccoli and cook until warmed through. Serve the beef and broccoli over a bed of cooked white rice with extra sauce from the pan spooned over top.