Preheat the oven to 375 degrees F.
Cut the top off of the tomatoes and clean out all of the pulp, leaving a 1/2-inch thick skin. Reserve the pulp. In a medium saute pan, heat 1/4 cup of the olive oil over medium heat. Add the onion and saute until the onions are golden brown, about 5 minutes. Add the garlic, reserved tomato pulp, and rice, and simmer for 5 minutes. Add the lamb, pine nuts, parsley, dill, salt, and pepper. Stir to combine and continue cooking until lamb is browned.
Fill the tomatoes with the lamb mixture, sprinkle the tops with cheese, and drizzle with the remaining 4 teaspoons of olive oil. Place in a 9-by 13-inch baking dish. Pour water in the bottom of the dish and bake for 1 hour. Serve warm.
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