Preheat broiler to high.

In the bowl of food processor fitted with a metal blade, pulse the garlic, salt, and rosemary. Add the cayenne, mint leaves, parsley leaves, and lemon juice. Pulse. With the machine running, slowly pour in the olive oil and allow the mixture to fully combine.

Transfer one-third of the pesto to a small bowl and reserve for serving after the chops are cooked. Pour the rest into a second bowl.

Place the lamb chops on a broiler pan. Lightly brush both sides of the lamb chops with the pesto.

Broil the lamb chops, 6 - 8 inches from the heat, for 7 minutes. Turn the lamb chops over and broil for another 3 minutes.

To serve, place 3 lamb chops on each plate, add remaining pesto to finished chops.