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Heat 1 teaspoon of oil in a large frying pan over medium heat. Add the broccoli and cook for approximately 4 minutes or until tender.
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Add the ginger and garlic to the pan and cook for 30 seconds more.
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Remove the broccoli from the pan; place on a plate and cover.
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Wipe the pan clean with a paper towel and turn the heat to high. Add the remaining tablespoon of oil.
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Season the steak pieces with salt and pepper and add them to the pan in a single layer – you may need to do this step in batches. Cook for 3-4 minutes on each side until browned and cooked through.
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Add the broccoli mixture back to the pan and cook for 2 more minutes or until warmed through.
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In a bowl whisk together the oyster sauce, beef broth, sugar, sesame oil and soy sauce. In a small bowl mix the cornstarch with a tablespoon of cold water.
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Pour the oyster sauce mixture over the beef and vegetables; cook for 30 seconds. Add the cornstarch and bring to a boil; cook for 1 more minute or until sauce has just started to thicken.
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Serve immediately, with rice if desired.