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Combine the soya sauce and balsamic vinegar in a medium bowl and set aside.
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Place the steak in a container and coat with 1 tbsp of flour. Add 2 tbsp of the soya sauce and balsamic vinegar mixture to the steak mixture. Turn the meat around in the container until evenly distributed. Set aside for at least 20 minutes.
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Take the remaining soya sauce and balsamic vinegar mixture and add 2 tbsp flour, chicken broth, brown sugar, rice vinegar, sesame oil, garlic, ground ginger and chili pepper flakes. Whisk to combine.
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Heat a non-stick frying pan over high heat. Add the water and broccoli to the pan and cover with a lid. Steam the broccoli until tender crisp. Remove from the pan and add the sliced pepper. Cook until tender crisp. Also remove from the pan.
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Add the olive oil to the frying pan and add the marinated beef to the heated oil in a single layer without over crowding. If the beef is crowded, do this in 2 batches, dividing the olive oil.
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Allow the beef to sear for about a minute on each side, until beef just barely cooked through. Remove the beef from the pan and set aside along with the broccoli and pepper.
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Add the soya sauce and balsamic vinegar mixture into the frying pan and allow it to thicken. This should take about 2-3 minutes. Return the broccoli, peppers and beef to the pan and stir to coat.
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Serve over cooked rice or egg noodles, garnishing with sesame seeds and green onions if you wish.