Preheat the oven to 350°F. Spray a 13×9×3-inch baking dish with cooking spray.
Bring a large pot of salted water to a boil. Add the thickly shredded cabbage and boil for 5 minutes. Drain and set aside.
In a medium saucepan, combine V8 juice and tomato paste, bring to a boil. Reduce heat and simmer for 5 minutes.
In a large bowl, mix the ground beef, diced onions, eggs, cooked rice and salt and pepper. *Over mixing will cause the meat to be tough.
Place half of the shredded cabbage in the bottom of the prepared baking dish. Pour 2 cups of the tomato sauce over the cabbage.
Add the meat mixture to the top of the cabbage and lightly press into place.
Add the remaining cabbage to the top of the meat mixture. Reserve 1 cup of the tomato sauce and pour the remaining sauce on top and cover with aluminum foil.
Place the baking dish on a cookie sheet and place on the middle rack in a preheated oven.
Bake for 90 minutes, remove foil, add the reserved tomato sauce and bake uncovered for an additional 30 minutes. Remove from oven and let sit for 10 minutes before serving.