In a large dish or Zip-top bag, combine the ingredients for the marinade. Add the beef slices and mix in until coated. Let sit for at least 10 minutes – the longer the better though!
In the interim, grab a small bowl, add all of the sauce ingredients and stir until blended. Set aside. In a saucepan, bring some lightly salted water to a boil. Add the broccoli and cook for 2 minutes. Remove from heat and drain thoroughly.
Next, in a large frying pan or wok over high heat, add the cooking oil and swirl to coat the pan. Add the beef, trying to create a single layer so that it cooks evenly and thoroughly. Let cook 1 minute. Flip beef slices (as best you can). Add the garlic to the pan, and fry for an additional 30 seconds or so until the beef no longer appears pink.
Add in the sauce and the broccoli and bring to an aggressive simmer.
Add in the flour* and cook until the sauce boils and begins to thicken (usually takes less than a minute!)