Cut any visible fat off the beef, and cut the beef across the grain into thin strips.
In a bowl, mix together the cornstarch, water, garlic, ginger and 1 teaspoon brown sugar. Add the beef to the mixture and stir to coat the beef. Cover with plastic wrap and set in the fridge to marinate for 30 minutes.
Cook the rice according to package instructions.
Whisk together the sauce ingredients in a small bowl and set aside.
Heat 1 teaspoon of oil in a skillet over medium-high heat, and cook the broccoli and green onions for 2 to 3 minutes, or until just tender-crisp.
Remove the broccoli and green onions from the skillet and set aside on a plate.
Cook the beef in the same skillet. You might need to spritz the skillet with a little nonstick spray. Actually, you might want to use 2 skillets, or divide the beef into two batches if you can. If you add too much beef to the skillet, the beef will just stew in the pan. If you cook the beef in two batches, it'll brown up nicely.
Let the beef sit in the hot skillet for a minute or two without touching it, just to get a good sear on it and let the sugar in the marinade caramelize a little bit. Then, stir-fry the beef for another 2 to 3 minutes, until the beef is almost cooked through (you should still see just a little bit of pink/blood)
Add the sauce to the skillet and stir it around with the beef for a minute until thickened.
Add the broccoli and green onions back to the skillet and stir to coat with the sauce.
Spoon the beef and broccoli over the rice to serve.