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.
Notes
Chicken: here is a skillet method for quick, cooked and shredded chicken.Doubling: a single recipe of this soup doesn't make a whole lot - I always double it for our family of seven (five kids, two adults). Of course, it goes a bit further if adding on toppings so keep that in mind. Cheese: originally the recipe was posted with mozzarella cheese. It's very yummy that way and occasionally I still use it but for the most part, I've changed to using Monterey Jack for a much creamier and smoother texture. Incidentally cheddar doesn't seem to work well here - it is a bit to greasy and doesn't melt well.Salsa: also, the salsa in this recipe is quite important - use a salsa that has great flavor as it is a key component to the soup. A salsa with a lot of heat is obviously going to make the soup spicy. I like to use a mild or medium salsa (Trader Joe's chunky sals or fire-roasted salsa are two of my favorites). And if you want to change it up a bit, using a green salsa is a wonderful variation. You can probably tell this soup is endlessly adaptable.Turkey: don't forget that leftover, cooked turkey is delicious in this soup. Celery Seed/Salt: I often sub celery seed (just 1/4 teaspoon) for the celery salt and then just add additional salt to taste if needed.