Begin by browning the ground beef in a large skillet with garlic and onion.
Add tomato sauce and broth. Bring to a boil, then turn down to simmer for about 30 minutes.
Carefully remove outer leaves of a green cabbage, making sure there are no tears.
Fill a shallow skillet with water, bring to a boil, then dip the cabbage leaves in to cook for just a minute or two until wilted. Remove from water and set aside.
Combine cooked rice, ground beef and Parmesan. Salt and pepper to taste.
Add about 1/2 cup of the meat-rice mixture to each cabbage leaf. Tuck the ends and roll. Place in a Pyrex baking dish. Add about 2 cups water.