In a large pot or Dutch oven, heat olive oil over medium heat. Add the ground beef and cook until browned, breaking it up as it cooks. Drain excess grease if necessary. Add diced onion and garlic, and sauté until softened, about 3–4 minutes.
Stir in the chopped cabbage. Cook for 5–7 minutes, stirring often, until the cabbage starts to wilt.
Pour in the diced tomatoes, tomato sauce, beef broth, cooked rice, paprika, oregano, thyme, salt, and pepper. Stir well to combine.
Bring the mixture to a gentle simmer. Cover the pot and let it cook for 25–30 minutes, stirring occasionally, until the cabbage is tender and the flavors are melded together.
Taste and adjust seasoning if needed. Garnish with chopped parsley before serving.