Prepare the Cabbage: Start by bringing a large pot of water to a boil. Use a knife to carefully cut out the core of the cabbage. Place the cabbage in the boiling water, and cook for 5-8 minutes, gently peeling off each leaf with tongs as it becomes tender. Place the leaves aside to cool.

Cook the Rice: In a small pot, bring 2 cups of water to a boil. Add the rice, reduce the heat, and simmer until the rice is tender and the water is absorbed. Set aside to cool.

Make the Filling: In a large skillet, heat the oil or butter over medium heat. Incorporate the chopped onions and sauté them until they turn translucent. In a large bowl, combine the ground beef, cooked rice, sautéed onions, eggs, salt, and pepper.

Assemble the Cabbage Rolls: Take one cabbage leaf at a time and place about 2 tablespoons of the meat mixture onto the center. Fold in the sides and roll tightly, tucking in the edges to keep the filling secure.

Prepare the Sauce: In a large pot, combine the tomato soup, tomato juice (or vegetable cocktail), and chicken broth. Stir well.

Cook the Cabbage Rolls: Place a layer of cabbage rolls in the pot with the tomato sauce, then layer more rolls on top, ensuring they’re covered by the sauce. Bring the pot to a gentle simmer, cover, and cook for 1.5 to 2 hours on low heat, until the rolls are tender and flavors are well blended.

Serve: Carefully remove the rolls from the pot and place them on a serving platter. Spoon some of the tomato sauce over the rolls for extra flavor, and serve hot.