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Bring a large pot of lightly salted water to a boil over high heat. Add the cabbage and cook, covered, until the outer layers of leaves peel off easily. Peel off the tender outer leaves and choose the 10 largest ones. (Save the remaining cabbage for another use, such as stir-frying.) Trim out the thick rib in the center of each leaf. In a medium saucepan of lightly salted boiling water, cook the rice for 5 minutes. Drain, rinse under cold, running water, and drain again. In a medium skillet, melt the butter over medium heat. Add the onion and cook, stirring often, until softened, about 5 minutes. Add the garlic and cook, stirring, for 1 minute. Transfer to a medium bowl, and mix in the parcooked rice, the ground beef, egg, savory, salt and pepper. Place about 1/3 cup of the filling in the center of a cabbage leaf, fold over the sides, and roll up into a cylinder. Place the roll on a plate, seam side down, and repeat with remaining leaves and filling. In a blender, process the tomatoes with their juice, the brown sugar, and lemon juice to a puree. Pour the sauce into a 3 1/2 quart slow cooker, and layer the cabbage rolls in the sauce. Cover and cook until the cabbage rolls are tender, 6-7 hours on low. Using a slotted spoon, transfer the rolls to a serving platter. Pour the sauce into a sauceboat and serve with the cabbage rolls.
