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Preheat the oven to 170°C. Finely slice the olives and using the back of a knife, turn them into a purée. Place the anchovy fillets on a chopping board and using the side of a kitchen knife, push down on them with a little force to turn them into a purée. Mix this purée with the olive oil and the olive purée.
Place the cherry tomatoes into an ovenproof dish, splash with olive oil and pop them into the oven. As they cook you can cook the lamb chops.
Heat a sauté pan or large frying pan and melt clarified butter (or you can use olive oil). Place the lamb chops into the hot, foaming butter and fry the chops for about three minutes on each side, turning once. While the chops cook, check to see how the tomatoes are doing.
Remove the chops from the heat, but keep them in the pan and the meat juices. Spread the anchovy-olive purée onto the top of each chop. The tomatoes should now be ready.
Place the tomatoes in the pan with the chops and serve.