Cut your thawed flank steak into strips, going against the grain of the meat. Toss steak strips in corn starch in a medium bowl and add remaining marinade ingredients: sesame oil, garlic, salt, paper, soy sauce, brown sugar, and lime. Mix and let sit for 45 minutes to 2 hours.
Let the steak come to room temperature. Bring olive oil to medium heat in a skillet or dutch oven on the stove. Add steak strips and cook to desired doneness. You can add more or less of the marinade in the skillet with the steak depending on how saucy you want your beef and broccoli to turn out. The cook time will depend on how thick your strips are, but about ten minutes should be an average cook time, stirring to help them cook evenly and to keep them from sticking to the pan.
Add your broccoli and cook another five minutes, until fully cooked, adding another tablespoon of olive oil if desired. Salt and pepper to taste. Serve with rice and garnish with green onion if desired.
If you like a spicier dish, you can add crushed red pepper or sliced fresh red peppers to this recipe, either in the marinade or with the broccoli.