Preheat the oven to 350 F. Grease a 2-quart baking dish or spray it with nonstick cooking spray.

Heat the oil in a large skillet over medium heat. Add the ground beef and cook for 3 minutes, stirring constantly. Add the onion and bell pepper and continue cooking until the beef is no longer pink and the onions are translucent. Add the garlic and cook for 1 minute longer. Drain and discard the excess fat.

Add the diced tomatoes, tomato sauce, vinegar, 1/2 teaspoon of salt, and the pepper. Stir to combine. Reduce the heat to low and simmer for 5 minutes. Set aside.

Meanwhile, coarsely chop the cabbage and place it in a large saucepan. Add 1 to 2 cups of water and 1 teaspoon of salt.

Place the pan over medium heat and bring to a boil. Reduce the heat to medium-low and cover the pan. Simmer for 10 minutes, or until the cabbage is tender.

Drain the cabbage and place it in the baking dish. Top the cabbage with the ground beef mixture.

Bake the casserole for 20 minutes. Top with cheese and continue baking for about 5 minutes, or until the casserole is hot and the cheese is melted.