Preheat oven to 350° and grease a 9"-x-13" baking dish with cooking spray. In a large dutch oven or pot over medium heat, heat oil. Add onion and cook until soft, about 5 minutes.Stir in garlic and cook until fragrant, 1 minute more. Add ground beef,breaking up meat with a wooden spoon, and cook until no longer pink, about 6 minutes. Drain fat.
Return beef mixture to skillet. Stir in tomato paste until beef is coated, then add chopped tomatoes, rice, and 2 cups broth.Season with oregano, salt, and pepper. Bring mixture to a simmer and cook 10 minutes, stirring frequently to prevent rice from scorching. Gradually stir in cabbage and cook until slightly wilted, 5 minutes. Stir in remaining 1 cup broth.
Transfer mixture to prepared baking dish and cover dish with foil. Bake until rice is tender, about 40 minutes. Garnish with parsley before serving.