Make the gremolata by blending the mint, parsley, garlic, capers, anchovy, 1/4 cup olive oil, and lemon juice in a blender or food processor (a mini food processor works best) until the texture of coarse pesto, scraping down the sides as needed. You can also finely chop the mint, parsley, garlic, capers, and anchovy by hand, put it into a medium bowl, and whisk in the olive oil and lemon juice.

Set a large, heavy skillet (cast iron is ideal) over medium-high heat. Pour a tablespoon or so of olive oil into the pan and swirl to coat the bottom. Set the chops into pan. The cooking time will vary based on the thickness of the chops. For medium-rare 1-inch-chops, cook for about 4 minutes until deeply browned. Turn them over and cook the second side about 4 minutes. Adjust the time if your chops are a little thinner or a little thicker. If you are unsure when the lamb is done, you can use an instant-ready thermometer and aim for an internal temperature of about 130 degrees F or use a paring knife to make a little incision in the center and have a peek. Keep in mind the chops will continue to cook once off the heat.