Chop the cabbage, removing the core and slicing it into 1-inch wide pieces.
Bring a large pot of salted water to a boil and cook the cabbage for 2 minutes. Drain well and set aside.
In a large skillet, brown the ground beef over medium heat. Stir in the diced onion, carrot, celery, garlic, red pepper flakes, and salt. Cook for 5 minutes.
Pour in 3 cups of the tomato juice and rice. Bring to a simmer and cook for 5 minutes. Stir in the grated Parmigiano cheese and half the chopped parsley. Adjust seasoning as needed.
Grease a 9 x 13 inch baking dish and preheat the oven to 350 degrees F.
Layer ⅓ of the cabbage in the dish, then half the beef mixture, and sprinkle with ⅓ of the mozzarella.
Layer half of the remaining cabbage, the rest of the beef mixture, and half of the remaining mozzarella.
Spread the rest of the cabbage, pour the remaining tomato juice over, and top with the last of the mozzarella.
Cover with foil and bake for 1 hour, then uncover and bake for an additional 15 minutes. Let rest for 15 minutes before serving.
Garnish with the remaining parsley and serve hot.