For the Marinade: In a 1 gallon ziploc bag, combine 1 tablespoon Green Za'atar and all the remaining marinade ingredients. Add the lamb chops and allow to marinate several hours in the refrigerator or one hour at room temperature.
For the Lamb Chops: Preheat the broiler on high.
Heat a large cast iron skillet on the stovetop over high heat and add olive oil to coat the bottom. Sear the lamb chops 2 minutes on each side.
Place the skillet under the broiler and cook 4 minutes more.
Allow the meat to rest a few minutes and garnish with the remaining Green Za'atar. Serve with your favorite spring greens and grain.