Set a heavy pot over medium heat and add 1 tablespoon of the olive oil. Add the diced red and green bell peppers with a pinch of salt and cook, stirring occasionally, until softened at the edges and lightly blistered, 4–5 minutes. Scoop the peppers to a bowl.
Add the remaining 1/2 tablespoon olive oil to the pot. Stir in the onion and cook until translucent, about 3 minutes. Add the garlic and cook 30 seconds more.
Push the onions to one side and add the ground turkey to the open space. Season with the salt and black pepper. Cook over medium-high heat, breaking it into small pieces, until no longer pink and lightly browned in spots, 5–6 minutes. Sprinkle in the dried oregano and smoked paprika and cook 1 minute to bloom the spices.
Return the peppers and any juices to the pot. Pour in the diced tomatoes (with juices), tomato sauce, and beef broth. Bring to a boil, then reduce to a lively simmer. Partially cover and cook 12–15 minutes to meld flavors, stirring once or twice and skimming any excess foam if needed.
Stir in the cooked rice and red wine vinegar. Simmer uncovered for 5 minutes to warm the rice and thicken the soup slightly. If you prefer a looser soup, add a splash more broth or water. Turn off the heat and let the pot rest 3 minutes before tasting and adjusting seasoning.
Ladle into bowls and serve hot. Optional: finish with a drizzle of olive oil or a sprinkle of fresh parsley.