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Add 2 tablespoons of oil and the sliced flank steak to a large skillet or wok over medium-high heat. Cook flank steak for 6-8 minutes, flipping over halfway through, or until it is no longer pink. Remove the steak from the skillet and set aside on a large plate.
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Add the remaining tablespoon of oil to the skillet and cook the bell peppers, onion, and broccoli over medium-high heat for 5-7 minutes.
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In a medium-sized bowl whisk together the soy sauce, sugar, ginger, garlic, ⅓ cup broth, Sriracha sauce, and sesame oil. Add the steak and the sauce to the skillet with the vegetables, reduce the heat to medium, and let simmer for 2-3 minutes.
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In a small bowl whisk together the remaining ⅓ cup of warm broth and 2 tablespoons of starch. Mix in the slurry water to the skillet, continuing to cook over medium heat for a couple of minutes until the sauce has thickened up.
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Serve beef and broccoli stir-fry over rice with toasted sesame seeds and sliced green onions. Enjoy!