Blot the anchovy fillets with a paper towel to remove excess oil. Mince them until they form a smooth paste. In a small bowl, combine the anchovy paste and grated garlic. Rub this mixture evenly over both sides of the lamb chops. Season lightly with salt and pepper. Let the meat sit at room temperature for 15 minutes to take the chill off.

Place your griddle over two burners set to medium or medium-high heat. Let it heat for 5 to 7 minutes. To test, drop a bead of water on the surface; it should dance and evaporate instantly. Lightly coat the surface with neutral oil using a heat-safe brush.

Place the lamb chops upright, fat side down, onto the hot surface for 1 minute, optional. Do not crowd them. Sear for 3 to 4 minutes on the first side until a deep, dark crust forms. Flip the chops and cook for another 2 to 3 minutes for medium-rare.

Cook time will vary due to the thickness of the lamb chops and individual ovens. Always check the temperature using an instant-read thermometer - go through the side of the chop and aim for the very center of the thickest part, making sure you stay away from the bone and the fat cap. Bone conducts heat differently from meat and will throw off your numbers.

While the meat rests, place the lemon halves, cut-side down, directly onto the griddle. Cook for 2 to 3 minutes until the flesh is caramelized and slightly blackened.

In your small saucepan over medium-low heat, add the olive oil and shallots. Sauté for 60 to 90 seconds until soft. Add the capers and stir for 20 seconds. Remove the pan from the heat. Stir in the parsley, mint, lemon zest, lemon juice, vinegar, and pepper. If the sauce looks too thick, whisk in an extra tablespoon of olive oil.

Arrange the rested lamb on a platter. Spoon the warm salsa verde generously over the chops. Serve with the charred lemon halves on the side for squeezing.