In a medium saucepan, heat the olive oil over medium heat. Add the onions and cook, stirring often, until they are translucent, about 5 minutes.
Add the remainder of the ingredients, except the cheese. Heat over medium heat, stirring occasionally, until the soup comes to a simmer. Reduce the heat so the soup is simmering but not vigorously boiling and add the cheese one small handful at a time, stirring to let each addition melt before adding the next.
Give the soup a good stir making sure all the cheese has melted. Season with salt and pepper to taste, if needed. Serve with additional toppings (optional): crushed tortilla chips, olives, sour cream, avocados, cilantro, tomatoes.
