Heat large pot over medium heat. When pot is warm, add olive oil and butter, and let butter melt completely.
When butter has melted, add onion, celery, carrots, and garlic to pot. Stir to incorporate, then sauté 5 to 6 minutes or until vegetables are tender. Add all-purpose flour and stir until flour is incorporated .
Add chicken broth, buffalo sauce, salt, and pepper. Stir well, then simmer 5 minutes or until soup begins to thicken.
Remove pot from heat. Add shredded chicken, cream cheese, and shredded cheddar. Stir until cheese begins to melt, then return pot to heat. Simmer, stirring occasionally, soup another 5 minutes, or until cream cheese is melted and incorporated into soup.
Portion soup into serving bowls. Add desired toppings and serve warm.
Recipe Notes
Cheddar Cheese: For the best results, skip the prepackaged cheese and shred your own from a block of cheddar.
Make it Gluten Free: Use gluten-free all-purpose flour, or replace the flour with arrowroot powder or tapioca starch. Make sure your chicken broth is completely gluten free, too.