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Place the thinly sliced beef into the bottom of your slow cooker.
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In a medium mixing bowl, whisk together the beef broth, soy sauce, brown sugar, sesame oil, minced garlic, and grated ginger until well combined.
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Pour the sauce mixture over the beef and stir gently to ensure all the meat is coated.
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Cover the crockpot and cook on low for 4 to 6 hours, or on high for 2 to 3 hours, until the beef is tender.
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About 30 minutes before you are ready to serve, whisk the cornstarch and cold water together in a small bowl to create a smooth slurry.
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Stir the cornstarch slurry into the slow cooker and add the fresh broccoli florets on top.
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Cover and continue cooking for another 20 to 30 minutes, or until the sauce has thickened and the broccoli is tender but still bright green.
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Give everything a final stir and serve the beef and broccoli over warm rice, garnished with sesame seeds and green onions if desired.