Bring a large pot of salted water to a boil. Put the cabbage into the boiling water, cover, and let boil gently for 4 to 5 minutes. Drain well.

Melt the butter in a saucepan, add the onion and garlic, and cook, stirring, only until the onion is soft, not browned. Add the tomato sauce, water, allspice, and salt and pepper to taste. Reduce the heat and let the sauce simmer for about 15 minutes. Taste and correct the seasoning. The sauce should be thickened, but not so thick that it “plops” when poured from a spoon.

Gently remove the tough outer leaves from the cabbage and reserve. Remove 12 more leaves to make the rolls. Chop the remaining cabbage coarsely and spread over the bottom of a 13×9-inch oiled baking dish. Sprinkle the brown sugar over the chopped cabbage, then sprinkle lightly with salt and pepper.

Preheat the oven to 350℉.

Combine three-quarters of the sauce with the rice and beef, and mix well. Divide the filling into 12 approximately equal parts and spoon each portion onto a cabbage leaf. Starting from the stem end, roll up each leaf, tucking in the sides, and place the roll on the chopped cabbage, seam-side-down. Spoon a little of the remaining sauce on top of each roll. Cover the top with the reserved outer leaves. Bake for 1 hour in the preheated oven. Discard the topping of outer leaves and serve with sour cream and warm applesauce.