Heat the oil in a large soup pot over medium-high heat. Add the onion and pepper and sauté until the veggies are soft, about 5 minutes. Add the garlic and cook for another 30 seconds.
Remove the casing from the chorizo sausages and add them to the pot. Cook, breaking the sausages into pieces, until they are fully cooked. Stir in the chili powder, salt, and cumin.
Add the broth, quinoa, salsa, black beans, and tomatoes and bring the pot to a boil. Reduce the heat, cover the pot, and simmer for 15 minutes.
Stir in the cheese, corn, cilantro, and lime juice. Once the corn is warm and the cheese has melted, taste and add more salt if needed. Serve the soup topped with any or all of the toppings.
