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In the insert of your slow cooker, whisk the beef broth, soy sauce, brown sugar, sesame oil, and garlic. Place beef in liquid and toss to coat.
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Cook on low for 6 hours.
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After the 6 hours, whisk together the cornstarch and water and add to the slow cooker. Stir and continue to cook for 30 minutes so the sauce can thicken.
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Add broccoli and toss together. The broccoli will cook within minutes.
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Serve over rice, if desired.