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 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 if you wish, but I like a regular blender to get it silky smooth. 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 all but ½ cup of the black beans - I like to leave this extra ½ cup to garnish the top of each bowl. Cook on low until the soup is heated through. Taste and season additionally if needed.
Serve in bowls and top with the remaining black beans, scallions, chives, tortilla chips, cilantro, cotija cheese and more.