Cut the broccoli into bite-sized pieces. Fill a medium sized pot with about an inch of water. Place that on the stove over medium heat and let that come to a slight boil.
Add the cut up broccoli, cover the pot, and steam for about 5-7 minutes, depending how you like the broccoli. Once cooked, remove from heat and drain. Then set aside.
Beef
Cut beef into cubes, about one inch by one inch. Place in a large bowl, drizzling with olive oil and tossing to coat. Sprinkle on the seasonings, tossing again to coat.
Heat a large pan over medium / medium high heat. Grease with cook spray. Once heated, add the minced garlic and ginger, cooking for about 2-3 minutes, until fragrant.
Add the cut up, seasoned beef to the pan and cook for a couple minutes on each side. It should only take about 10 minutes to cook the beef.
Sauce
While the beef is cooking, prepare the sauce. Combine all the ingredients for the sauce in one bowl, and the two ingredients for the slurry in another.
Once the beef is cooked, add the sauce to the pan, bringing to a slight simmer. Simmer the sauce with the beef for about 3 minutes, until slightly thickened.
Then, add the slurry and mix that into the sauce. Bring back up to a simmer and simmer again for another 3 minutes, until the sauce is to your desired thickness.
Either add the broccoli in and mix everything together or serve on the side. As mentioned, there will be plenty of extra sauce for the broccoli and rice.