In a resealable bag, combine the ingredients for the marinade. Add the steak and shake to coat. Seal the bag and refrigerate for at least 30 minutes or up to 24 hours.
Mix together the sauce ingredients in a bowl and set aside.
After the steak is done marinating, heat 2 tablespoons of the olive oil in a large skillet or wok over medium-high heat. Place the steak in the hot skillet and fry for 2 to 3 minutes, until cooked through, stirring often. Remove the steak from the skillet and set aside.
Add the remaining 2 tablespoons of olive oil and the broccoli, onion, and bell pepper to the skillet and saute for 2 minutes.
Return the steak to the skillet and reduce the heat to medium-low. Whisk the sauce and pour it over the beef. Give everything a quick stir and cook for 1 minute. The sauce will begin to thicken immediately.
Serve over cauliflower rice.