Heat a large pot over medium-low heat and add the olive oil. Stir in the onion, garlic, cumin, paprika, salt and pepper. Cook until the onions soften, about 5 to 6 minutes. Pour in the diced tomatoes and chicken stock and add the tortilla pieces. Bring the mixture to a boil, then reduce it to a simmer and cover. Simmer for 5 minutes.
Carefully transfer the mixture to a blender and puree until smooth. You could also use an immersion blender, but I find that they spray everywhere. Pour the soup back into the pot and heat it over low heat. Stir in the cheese, one handful at a time, until melted. Stir in the turkey (or chicken!). Cook on low until the soup is heated through. Taste and season additionally if needed.
Serve in bowls and top with avocado, radish, tortilla chips and the leftover cilantro.