Preheat oven to 375 degrees F.
Cut the tops of each pepper leaving the stems intact. Use a paring knife to cut away the seeds and ribs inside each pepper.
In a large bowl, combine the cooked rice, olive oil, cinnamon, allspice, garlic, mint, salt, pepper and lamb. Stuff into pepper cavities and top with pepper "lids". Arrange peppers in a large baking dish.
To make the sauce, heat olive oil in a medium saucepan. Add garlic and saute until softened, about 1 minute. Add diced tomatoes, tomato paste, spices and herbs. Taste and adjust seasoning, adding up to a total of 1 tsp cinnamon and 1 tsp allspice if you like more intense spice. Pour around peppers, then cover dish with aluminum foil and bake 1 hour, or until lamb is cooked through and peppers are soft.