Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and sauté for about 5 minutes, or until the onion is translucent.
Add the minced garlic and cook for an additional minute, stirring frequently to avoid burning.
Increase the heat to medium-high and add the ground beef. Cook until browned, breaking it apart with your spoon, about 5-7 minutes.
Stir in the diced carrot and green bell pepper, cooking for another 3-4 minutes until they begin to soften.
Pour in the diced tomatoes with their juice and the broth. Stir well to combine all ingredients.
Bring the mixture to a boil, then add the chopped cabbage, thyme, oregano, salt, pepper, uncooked rice, and tomato paste.
Reduce the heat to low, cover the pot, and simmer for about 20-25 minutes, or until the rice is cooked and the cabbage is tender.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.