Preheat oven to 350 degrees.
Bring a large saucepan of water to a boil. Add the cabbage; cook for 4 to 5 minutes then drain and set aside to cool. Carefully remove whole leaves.
In a small saucepan, combine beef broth, tomato paste and green chilies over medium heat; simmer for 3 to 4 minutes then remove from heat and set aside. Heat the oil in a large skillet over medium heat; add the onion and cook for 2 minutes or until translucent. Add ground beef, crumbling with a spoon as it cooks. When beef is almost cooked through, add garlic and all seasonings (cumin through black pepper).
Cook, stirring well, for 1 minute. Add water and cook until excess liquid has evaporated. In a 9- x 13-inch baking dish, place a thin layer of sauce mixture, followed by a single layer of cabbage leaves. Next, layer half of the meat mixture then one-third of the sauce, followed by another layer of cabbage leaves. Repeat this process once more, finishing with sauce. Bake for 35 minutes and serve