Preheat the oven to 450 degrees F. Place the oven rack in the lower third of the oven so the lamb will sit in the middle of the oven.
Peel 6 of the cloves of garlic and place them in the bowl of a food processor fitted with the steel blade. Add the rosemary, 1 tablespoon salt, 1 teaspoon pepper, and butter. Process until the garlic and rosemary are finely minced. Thoroughly coat the top and sides of the lamb with the rosemary mixture. Allow to sit at room temperature for 30 minutes to 1 hour.
Toss the potatoes and remaining unpeeled garlic in a bowl with the olive oil and sprinkle with salt. Place in the bottom of a large roasting pan. Place the lamb on top of the potatoes and roast for 1 1/4 to 1 1/2 hours, or until the internal temperature of the lamb is 135 degrees (rare) or 145 degrees (medium). Remove from the oven and put the lamb on a platter; cover tightly with aluminum foil. Allow the lamb to rest for about 20 minutes. Slice and serve with the potatoes.