How to Make It
Preheat the oven to 200°. Spread the olive oil on a rimmed baking sheet and sprinkle with the thyme and a large pinch each of salt and pepper. Arrange the tomatoes on the sheet in a single layer and bake for 2 hours, or until slightly dried and firm. Transfer to a bowl and stir in the olives, garlic, lemon zest and basil.
Raise the oven temperature to 450°. In 2 heavy-bottomed ovenproof skillets, heat the vegetable oil until almost smoking. Season the chops with salt and pepper and cook over moderately high heat until well browned on the bottom, about 3 minutes. Turn the chops and cook for 1 minute. Transfer the skillets to the oven and roast for about 6 minutes for medium rare. Set the lamb on plates and serve with the tomato relish and a wedge of Mashed Potato Cake.