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Marinate the meat: In a large ziploc bag, combine steak, soy sauce, brown sugar, mirin, sesame oil, garlic, lemon juice, paprika, and pepper. Seal and shake to combine. Leave in fridge to marinate 1 hour to overnight.
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Steam the vegetables: Add 1 inch of water to a large pot. Add the broccoli and baby bok choy. Cover and turn the heat to high. Steam vegetables 4-6 minutes, depending where you like your veggies on the crunchy versus tender scale.
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While vegetables are steaming, cook beef. Heat grapeseed oil in a wok or nonstick skillet over medium-high heat. Remove steak from marinade and add to the wok. (Discard excess marinade.) Cook, stirring often, until browned, 5-8 minutes.
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To serve: Put 1 cup of rice in the bottom of each serving bowl. Divide beef and vegetables between bowls. Top with scallions and sesame seeds.