Combine first 7 ingredients in a bown, toss with lamb pieces, and put in a ziploc bag in the refrigerator for at least an hour.
Heat olive oil in large skillet till smoking.
Add lamb and cook on high till caramalized. Add red onions and pepper, cook till tender, and add tomatoe, cumin, and mint and cook for another couple of minutes. Remove lamb from skillet and keep warm in serving dish.
Deglaze skillet with water or broth. Add broccoli to skillet, add more water, cover and steam till crisp/tender.
At this point, the lamb can be added to the broccoli or the two may be served separately. The dish can be served over rice or even pasta.
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