Fry half the chopped onion in olive oil for 3 minutes, then add half the chopped garlic and fry for another 2 minutes, stirring occasionally over low heat. Add tomatoes, sugar, mix and cook over low heat for 10 minutes. At the end, add wine vinegar, stir and turn off the heat.
Preheat the oven to 360 F. Put cabbage leaves into boiling water and boil for 3-4 minutes just until pliable. They should become soft, but at the same time remain whole. Transfer soft leaves to a bowl of ice cold water.
In a bowl, put the ground beef, cooked rice, salt, spices, remaining garlic, softened onion and egg. Mix everything thoroughly.
When the cabbage leaves have cooled, cut off the top of the central white strip (if stiff) to soften the leaf. Put 2 tablespoons of minced meat on the edge of the cabbage leaf.
Gently but tightly wrap the minced meat in cabbage. Repeat with the remaining leaves and filling. Put 4-5 tablespoons of tomato sauce on the bottom of the baking dish. Lay stuffed rolls on top with seam side on the bottom so they don't unroll.
Top with the remaining tomato sauce. Cover the baking dish with foil and put in the oven for half an hour. After half an hour, remove the foil and bake for another 20 minutes.