In a large pot, heat the olive oil over medium heat. Add the chopped onion and garlic, and sauté until the onion is translucent, about 3-4 minutes.
In a bowl, combine the ground beef or turkey, uncooked rice, oregano, paprika, salt, and pepper. Mix well and form into small meatballs, about 1 inch in diameter.
Add the diced carrot and chopped cabbage to the pot with the sautéed onion and garlic. Stir to combine and cook for another 5 minutes until the vegetables begin to soften.
Pour in the broth and diced tomatoes, then bring the mixture to a boil.
Carefully add the meatballs to the boiling soup. Reduce the heat to low and let it simmer for about 25-30 minutes, or until the meatballs are cooked through and the rice is tender.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.