Preheat the oven to 350°F (175°C).
Blanch the cabbage leaves in boiling water for about 3-4 minutes or until they are soft and pliable. Remove and set aside.
In a mixing bowl, combine the ground beef, cooked rice, chopped onion, salt, black pepper, allspice, and egg. Mix well.
Place a spoonful of the beef mixture on each cabbage leaf and roll up tightly, tucking in the sides to form a neat package.
Arrange the cabbage rolls in a large baking dish.
In a separate bowl, whisk together the beef broth, tomato paste, brown sugar, red wine vinegar, and water until well combined.
Pour the mixture over the cabbage rolls, making sure they are fully covered.
Cover the dish with aluminum foil and bake in the preheated oven for 1 hour and 30 minutes or until the cabbage rolls are fully cooked and the sauce has thickened.
Remove from the oven and let cool for a few minutes before serving.