Slice the onions into medium sized pieces. Wash the broccoli and cut into bite sized pieces about 1/2-1 inch thick. Slice the steak into one inch pieces as well (steak is easiest to cut when it is slightly frozen). Mix all of the sauce ingredients together in a bowl and set aside.

In a large saute pan, bring the stove to high heat. Drizzle a few tablespoons of oil into the pan and begin sauteing the onion until it begins to caramelize. When the onions are soft, add the pieces of steak and saute until the steak is nearly all cooked through (still slightly pink--don't over cook or it will be too tough). Remove the steak and onions and set aside.

Add more oil to the pan and place the broccoli pieces into the pan. Season with salt and pepper. When broccoli is hot, add a few tablespoons of water and let broccoli begin to steam. Once the broccoli is slightly soft, but still very green, remove from the pan and add to the steak and onions. In the same pan, add the sauce ingredients and whisk on medium heat until sauce begins to thicken (about 1-2 minutes). Once sauce is thick, add the broccoli, steak and onions back to the pan and keep warm until ready to serve. Serve beef and broccoli over cooked rice.