How to Make It
Light a grill or preheat the oven to 375°. Season the lamb with salt and pepper.
If grilling, melt the butter in the olive oil in a small saucepan. When the coals are covered in white ash, grill the lamb over low heat for about 40 minutes, turning every 2 to 3 minutes and brushing the racks with the rosemary sprigs dipped in the butter mixture. The lamb is done when an instant-read thermometer inserted in the thickest part of the meat registers 125° for rare.
If pan-roasting the lamb, melt 1 tablespoon of the butter in 1 tablespoon of the oil in a large ovenproof skillet. Add the lamb racks, fat sides down, and cook over moderately high heat until the racks are browned all over, about 5 minutes. Add the rosemary sprigs and the remaining 1 tablespoon each of butter and oil to the skillet. Spoon some of the fat over the lamb. Roast for about 30 minutes, basting once or twice with the rosemary sprigs and fat and turning the racks halfway through. The lamb is done when an instant-read thermometer registers 125° for rare.
Transfer the lamb to a cutting board and let rest for 10 minutes. Carve the racks into chops. Sprinkle with the chopped thyme, mint and parsley and serve.