Preheat oven to 450 degrees. Pulse garlic, cheese, breadcrumbs, lemon juice, 1 teaspoon salt, and some pepper in a food processor until combined. Add fruit and onions. Pulse a few times, keeping mixture chunky.
Lay lamb flat on a work surface, skin side down. Season with salt. Spread artichoke mixture over top, leaving a 1/2-inch border. Tightly roll lamb, and tie with kitchen twine at 2-inch intervals to hold.
Rub lamb with oil, and season generously with salt and pepper, rosemary. Transfer to a roasting pan fitted with a roasting rack, and add water to pan. Roast for 30 minutes. Reduce oven temperature to 350 degrees. Continue to roast until an instant-read thermometer reaches 130 degrees to 135 degrees (for medium-rare), 1 hour to 1 hour 15 minutes. Baste with molasses. Let rest for 20 to 30 minutes before carving. Serve with mint sauce.