Heat your oven to 350°F and grease a 9×13 inch casserole dish well.
Cook the ground beef, chopped onions, and minced garlic in a skillet over medium heat until the meat is browned and crumbled, about 5-6 minutes.
Stir in the uncooked rice into the beef mixture and remove from the heat.
In a bowl, mix together the tomato sauce, vinegar, brown sugar, Worcestershire sauce, salt, and black pepper.
Spread one third of the shredded cabbage evenly at the bottom of the prepared dish.
Add half of the beef and rice mixture over the cabbage layer.
Pour one third of the tomato sauce mixture over the beef and rice.
Repeat with another one third of the cabbage, the remaining beef and rice mixture, and then another third of the sauce.
Top everything with the last third of the cabbage and the remaining sauce.
Cover the casserole tightly and bake it for 45 minutes.
After baking, remove the cover and continue cooking for an additional 15 to 30 minutes until the cabbage softens, rice finishes cooking, and the dish is bubbling.
Once done, gently mix the layers before serving warm.