Add the onion and cook, stirring occasionally, for 6 minutes until tender and translucent. Add the ground beef and cook, stirring and breaking up the beef, until browned and fully cooked.
Add the green chiles, garlic, chili powder, cumin, and salt. Stir well and let cook for 1 minute. Add the tomato sauce, black beans, and broth. Stir and bring to a boil. Reduce heat to low and simmer for 20 minutes.
To serve: Place 1/2 cup crushed tortilla chips in the bottom of a large soup bowl. Ladle hot soup over the tortilla chips. Add additional toppings to each bowl as desired: Diced avocado, chopped cilantro, diced jalapeno, and sliced radish.