Fry ground beef and onion in a large, high sided skillet until beef is no longer pink and onion is soft. Drain excess fat.
Add tomatoes, broth, Italian seasoning, and salt & pepper to taste. Bring to a boil. Stir in white rice. Add water if you think there's not enough for the rice to cook. Return to boil, reduce heat and simmer for 20 minutes, checking to make sure it's not getting too dry--the rice must absorb enough liquid. If necessary, add some more water. Excess liquid can be cooked off if you add a little too much.
Once beef/rice mixture is done, if you don't have much liquid left, add about 1/2-3/4 cup water. Layer cabbage over beef mixture and adjust temperature so the cabbage will steam. Allow to cook about 10-15 minutes, or until cabbage is cooked. Check occasionally to make sure there is enough liquid to maintain the steam and keep it from burning.