In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Add the minced garlic and ground beef (or turkey) to the pot. Cook until the meat is browned, breaking it apart with a wooden spoon, about 5-7 minutes. Drain excess fat if necessary.
Stir in the chopped cabbage and cook for an additional 5 minutes, stirring frequently until the cabbage begins to wilt.
Add the diced tomatoes (with juice), beef broth, uncooked rice, tomato paste, Worcestershire sauce, thyme, smoked paprika, salt, and pepper. Stir well to combine.
Bring the soup to a boil. Reduce the heat to low, cover the pot, and let it simmer for about 25-30 minutes, or until the rice is cooked and the cabbage is tender.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley if desired.