Season lamb with salt and pepper allow to come to room temperature (about 20-30 minutes) while you preheat your grill and make the pistachio basil pesto.
Prepare grill for high heat (450°F).
Cover the bones of the lamb with foil (to prevent charring) and place on grill. Close grill and let cook for 7 minutes, flip and cook for another 5 minutes, or until the internal temperature reaches 145°F for medium-rare.
Let lamb rest 10 minutes. Cut into individual chops.
Pistachio Basil Pesto
Place garlic in blender or food processor and pulse until chopped. Add pistachios, basil, lemon juice and salt and pulse until pistachios are finely chopped. Slowly stream in olive oil and process until combined. Add cheese and pulse briefly to just combine.