Add celery, carrot and onion. Simmer 25 minutes until veggies are soft but not mushy.
Meanwhile, melt butter in a skillet over low heat. Add flour and stir constantly with wire whisk, until smooth and free of limps. Cook this roux 8 to 10 minutes, still over low heat, whisking constantly to prevent scorching.
Turn the heat down under the broth to medium-low. Add the roux to the broth. Continue to whisk until smooth and thick about 5 minutes.
Slowly add Cheez Whiz and grated cheeses. Continue cooking until cheese is melted, whisking occasionally.
Heat milk in microwave until warm. Add to soup slowly. Whisk until smooth. You can add more milk if needed for desired consistency.
Serve with toasted croutons or crackers. Refrigerate leftovers.