In a large pot or Dutch oven, brown the ground beef, breaking it apart with a spoon until fully cooked.
Add the diced onion to the pot with the beef. Stir frequently and cook until the onion softens, about 5 minutes. Stir in the garlic and cook for 1 more minute.
Add the chopped cabbage, diced tomatoes with their juice, tomato sauce, beef broth, paprika, oregano, thyme, salt, and pepper. Simmer the mixture.
Cover the pot and simmer for 15 to 20 minutes, stirring occasionally, until the cabbage becomes tender.
Push the cabbage to one side of the pot. Stir in the uncooked rice. Cover and cook on low heat for 15 to 20 more minutes, until the rice is fully cooked. Taste to ensure the rice is tender.
Remove the pot from the heat once the rice is cooked and the cabbage is tender. Taste and adjust the seasoning with more salt and pepper as desired. Let the dish stand for a few minutes to absorb any remaining liquid.
Top each serving with fresh parsley.