Place the flank steak into the freezer for 10 minutes, this will help make it easier to cut into thin slices. Remove the beef from the freezer and slice it into ¼-inch thick slices, going against the grain. Season the meat evenly with salt and pepper.
Prepare the Hunan Sauce by whisking together beef broth, soy sauce, oyster sauce, rice vinegar, honey, chili paste, and cornstarch in a small bowl until the cornstarch is fully dissolved. Set aside.
Heat the oil in a large pan over high heat. Once the oil sizzles when a drop of water is added add the steak to the pan in a single layer–don’t crowd the pan. Cook in batches if needed. Cook for 3-4 minutes per side or until browned. Remove the seared beef from the pan and place it on a plate.
If the skillet is dry, add 1 teaspoon of additional canola oil. Add the broccoli, peppers, and onion to the pan. Cook for 4-5 minutes or until the vegetables are just slightly tender. Add the garlic and cook for 30 seconds more.
Add the beef back to the pan with the vegetables.
Whisk the reserved sauce again to be sure fully incorporated, and then pour the sauce over the beef and vegetables. Bring the mixture to a gentle boil, and cook for 1-2 minutes or until sauce has thickened.
Serve over rice with chopped green onions.