Preheat oven to 350 degrees. Spray a 9×13-inch baking dish with nonstick cooking spray.
In a large skillet over medium heat, cook the ground beef, onion, and garlic until the beef is browned and cooked through. Drain excess grease if needed.
Stir in oregano, thyme, paprika, salt, pepper, water, Worcestershire sauce, diced tomatoes, and tomato sauce. Simmer for 15 to 20 minutes. Remove from heat and stir in the cooked rice.
Heat olive oil in a large skillet or Dutch oven over medium heat. Add the cabbage and cook, stirring occasionally, until just tender, about 5 minutes.
Spread half of the cabbage in the prepared baking dish. Top with half of the meat mixture. Repeat with remaining cabbage and meat mixture.
Cover tightly with foil and bake for 40 minutes.
Remove foil, sprinkle cheese evenly over the top, and bake uncovered for 20 minutes, or until the cheese is melted and lightly browned.
Garnish with fresh parsley if desired. Let rest briefly before serving.