Place a large, deep skillet or saute pan (or Dutch oven) over medium heat. When the pan is hot, add about 1 tablespoon of vegetable oil or butter and then add the ground beef. Break up the beef with a spatula and cook, stirring, for about 2 to 3 minutes. Add the onion and continue cooking, stirring, until the beef is no longer pink and the onion is translucent.
Add the cabbage to the ground beef mixture along with the stewed tomatoes, diced tomatoes, tomato sauce, sugar, and vinegar. Cook, stirring, for about 5 minutes or until the cabbage is slightly wilted.
Add the water and rice to the beef and cabbage mixture. Reduce the heat to low, cover, and simmer until the rice is tender, or about 20 to 25 minutes. Add more water, if needed.
Taste and add salt and freshly ground black pepper, to taste.