Heat olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and minced garlic, sautéing until the onion is translucent, about 3-4 minutes.
Add the ground beef (or turkey) to the pot, breaking it apart with a wooden spoon. Cook until the meat is browned, about 5-7 minutes.
Stir in the chopped cabbage and continue to cook for another 5 minutes, until the cabbage begins to wilt.
Add the diced tomatoes (with their juice), beef or vegetable broth, uncooked rice, smoked paprika, Italian seasoning, salt, and pepper.
Bring the soup to a boil, then reduce the heat to low. Cover the pot and simmer for 30 minutes, or until the rice is tender and the cabbage is cooked down.
Taste and adjust seasoning if needed.
Serve the soup hot, garnished with fresh parsley.