Rub the racks of lamb with 3 tablespoons of the olive oil and 2 tablespoons of the herbs. Refrigerate and marinate overnight.
Preheat the oven to 450°F.
Heat a large ovenproof pan over medium-high heat, add the remaining 2 tablespoons olive oil, and sear the lamb on all sides. Transfer to the oven and roast for 8 to 12 minutes, or until slightly less than the desired degree of doneness. Remove the pan from the oven and allow the lamb to rest for 5 minutes.
Meanwhile, put the remaining 1 tablespoon herbs in a small piece of cheesecloth and tie with kitchen string to form a sachet. Put the reduced meat juices in a small saucepan and bring to a simmer over medium heat. Then put the sachet in the sauce and simmer for 3 minutes.
Slice each rack between the bones just prior to serving. Season with salt and pepper to taste. Remove the sachet from the juices and pour the sauce over and around the chops. Serve with the hot, golden, and crisp polenta.